Skip to main content

Full text of "Francisci Tessanek ... Elementa physicae, pars Ima"

See other formats 


Google 


This  is  a  digital  copy  of  a  book  that  was  prcscrvod  for  gcncrations  on  library  shclvcs  bcforc  it  was  carcfully  scanncd  by  Googlc  as  part  of  a  projcct 

to  make  the  world's  books  discoverablc  onlinc. 

It  has  survived  long  enough  for  the  copyright  to  cxpirc  and  thc  book  to  cntcr  thc  public  domain.  A  public  domain  book  is  one  that  was  never  subjcct 

to  copyright  or  whose  legal  copyright  term  has  expircd.  Whcthcr  a  book  is  in  thc  public  domain  may  vary  country  to  country.  Public  domain  books 

are  our  gateways  to  the  past,  representing  a  wealth  of  history,  cultuie  and  knowledge  that's  often  difficult  to  discovcr. 

Marks,  notations  and  other  maiginalia  present  in  the  original  volume  will  appear  in  this  flle  -  a  reminder  of  this  book's  long  journcy  from  thc 

publishcr  to  a  library  and  fmally  to  you. 

Usage  guidelines 

Googlc  is  proud  to  partncr  with  libraries  to  digitize  public  domain  materials  and  make  them  widely  accessible.  Public  domain  books  belong  to  thc 
public  and  wc  arc  mcrcly  thcir  custodians.  Nevertheless,  this  work  is  expensive,  so  in  order  to  keep  providing  tliis  resource,  we  liave  taken  stcps  to 
prcvcnt  abusc  by  commcrcial  partics,  including  placing  lcchnical  rcstrictions  on  automatcd  qucrying. 
Wc  also  ask  that  you: 

+  Make  non-commercial  use  ofthefiles  Wc  dcsigncd  Googlc  Book  Scarch  for  usc  by  individuals,  and  wc  rcqucst  that  you  usc  thcsc  filcs  for 
personal,  non-commercial  purposes. 

+  Refrainfivm  automated  querying  Do  nol  send  aulomatcd  qucrics  of  any  sort  to  Googlc's  systcm:  If  you  arc  conducting  rcscarch  on  machinc 
translation,  optical  character  recognition  or  other  areas  where  access  to  a  laige  amount  of  tcxt  is  hclpful,  plcasc  contact  us.  Wc  cncouragc  thc 
use  of  public  domain  materials  for  these  purposes  and  may  be  able  to  help. 

+  Maintain  attributionTht  GoogXt  "watermark"  you  see  on  each  flle  is essential  for  informingpcoplcabout  thisprojcct  and  hclping  thcm  lind 
additional  materials  through  Google  Book  Search.  Please  do  not  remove  it. 

+  Keep  it  legal  Whatcvcr  your  usc,  rcmember  that  you  are  lesponsible  for  ensuring  that  what  you  are  doing  is  legal.  Do  not  assume  that  just 
bccausc  wc  bclicvc  a  book  is  in  thc  public  domain  for  users  in  the  United  States,  that  the  work  is  also  in  the  public  domain  for  users  in  other 
countrics.  Whcthcr  a  book  is  still  in  copyright  varies  from  country  to  country,  and  wc  can'l  offer  guidance  on  whether  any  speciflc  usc  of 
any  speciflc  book  is  allowed.  Please  do  not  assume  that  a  book's  appearancc  in  Googlc  Book  Scarch  mcans  it  can  bc  uscd  in  any  manncr 
anywhere  in  the  world.  Copyright  infringement  liabili^  can  be  quite  severe. 

About  Google  Book  Search 

Googlc's  mission  is  to  organizc  thc  world's  information  and  to  makc  it  univcrsally  acccssiblc  and  uscful.   Googlc  Book  Scarch  hclps  rcadcrs 
discovcr  thc  world's  books  whilc  hclping  authors  and  publishcrs  rcach  ncw  audicnccs.  You  can  scarch  through  thc  full  icxi  of  ihis  book  on  thc  wcb 

at|http://books.qooqle.com/| 


^  -^ 


3lfe,. 


f . 


v^. 


y  < 


/ 


W 


M^ 


# 


>^- 


r 


Itj^ 


ut 


.  Jf 


/' 


k  ^-. 


M 

s 


X     V 


4' 


-    'J 


/ 


/ 


X 


l/ 


/ 


A 


^     1       . 


l 


FRAMCISCIJTESSANEK 

s.  r 

PHILOSOPHl^  DOCTORIS,  PRO- 
FESSORIS ,  ti  EXAMINATORIS 
I  REGII 

ELEMENTA 

PHYSIC^ 

P  A  R  S  I"" 


OLOMUCII 


TmS  JOSEPHff:  HIRNLIANK  ,    MARTINQ 

FKANCISCO  KARLETZKY  FACTOEE : 

ANNO  M.DCC.LXVIU1 


iem  em  fortefsrtem^  qm  ROGERIUS 
IjOSKOWlCa.  e  S.  /.  ;  fummis  Me 
tae  mfbrt  Gtomeiris  accenfeitdusy  ab  Eo 

J  Omnem  iiSrmm  bretviter  dare  co- 

mi^yiK  Hhicide;  fcribo  emm  leOiffimdDi' 
fnfidmm  Carond^  qm  dcffiuium  PbUofy- 
fbicorum  obJcurUatem  oderuiU  tum  mnuSy 
qusm  proHxUaiem, 

Si  fuarido  tmen  a  propofid  breviti^ 
te  nonM  defiSoy  vemm  dabif  Bene- 
«vobisLeSor.  Urgebad^ala  affiduo  inge- 
rentes :  Tjrombus  nunqum  foHs,  Ah» 
ittta  jitbinde  dcfuiefcendm  erat. 


PARS 


#1 


A 


f 


Confpedius  Qperis, 


°  Elemeiita  Pbjfic^  m  tres  farUs 

diftritm  :  Prma  nnfltScr 
r 
eorpus  generalim  fumptum ,  if  flerafque 

i^eSumes  eui^vis  cerfori  eommts.    M 

fecundam  e<voco  corfora  lotalia.    M  ter- 

tiam  fartiaUa.    Pars  prima  Pbjficamge. 

neralemabfolvit;  fecmla,  &  tertia^. 

eialem. 

Pheuit,  plaeere  immo  dehuii  Sjfiem 

f^»^pr*fiatit^iISAAa  NEWTONV 


St  Se^io  t  Caput  t    \ 

CoroU.  Ergo  etiam  rationes  sqiiales  uni  jti^  CaWt 
^uales  inter  fe ;  in  rationibus  ^nim  ^e£latur  quaiuitas 
cxponentis* 

V.  ^quftlia  fii^qdalibiiis  rubftitui  pofTuilt. 

YI.  Si  quantitates  inter  fe  aequales  «qnalifef 

augearttur,  vel  iminuantUr,  €tiaim  audac  vel 

minuts  manent  tfquales, 

CoroU^  Ergb  0ve  d^^tialibUs  ^q^ialia  addas  ,  Gve  ab  «* 
qualibus  ftqualia  demAs  ;  Icitnper  funima  aut  dijferenfia 
erunt  aequales»  II»  Sive  quantitates  «quales  per*cail- 
dem  ,  vel  aequaleitt  ^wantitatem  viultiplites ,  feu  drSidas : 
iterum  /tfStf,  aut  gfciow  «jjnaburttur  inter  ft. 

VII.  S^  quantitates  inter  fe  insquales  «qualiter 
augeantur,  velmihuantur,  nlanebunt  fem- 
per  inxquales  ;  fed  tamen  in  eadem  ratione, 
in  qua  prius  ef ant  quantitates  nondum  audar^ 
vel  imminuta:* 

Scbol  Quod  ultiraum  dixi»  tetlitts  ad  theoremata  r^- 
fertur,  quam  axiomata  ;  planeque  idem  cft  cum  illo  :  Si 
ejusdem  rationis  G.  tertnini  per  eaudem  quantitatem  muU 
tiflicentur  ,  aut  dividanmr ,  fada  vei  quoti  manebunt  in 
tadem  ratione. 

Leges  motus. 

^.2.  LEXL  Corpus  omnc  perfeverat  in  JlaiU 
Jcu  ijuictif,  fiu  motus  uniformitcr  in  dirc£lum^  nifi  a 
viribus  imprcjfis  (  five  a  caufa  movente  )  cogatur 
ftatum  fiium  immutarc.  Sic  Mctaphyfici.  Pro- 
batur  breviter  imo  :  Omn€  corpus  perfeverat 
inftatu  quietis,x\\(\  &c.  quia  dum  corpus  quiefcit, 
visejus  mptrix  admotumdeterminata  nonelt ; 
fcd  ncque  fe  ipfam  detcrminare  poteft  ,  cum 

agc- 


JUges  mtu$l  3 

agere  ex  determinacione  propri^  (blts  /piriri-" 
bus  proprium  (ic ;  ergo.  2do ;  Omne  corpns 
perfeverac  fnfiatu  motus ,  quia  dum  movetur^ 
visejus  mocrix  eft.decerminata  admocum,non 
ad  quiecem  }  deccrminacio  h«c  eft  racio  fuffi- 
ciens  mocus»  non  quiecis ;  proinde.  ^cio :  Om« 
ne  corpus  perfeverac  in  Jiatu  motus  mnijmrmittr  in 
JinBum ;  quia  dum  movecurydecerminatumeft  • 
ad  cercam  dirtHionem^  &  cercum  aleritatis  ff^s-^ 
dum^j  ergo  uc  alicer  moveacury  opus  eft  nova 
decerminacione ;  quare  cum  corpus  (e  ipfum 
decerminare»  h.  e«aliquam  (tacus  fuimucacio- 
nem  iibi  ipfi  inducere  nequeac ,  eadem  conct- 
nuo  diredione,  &  celericace  ferri  debec ,  niil. 
&c. 

CbroO.  Ex  djica  lege  fluQnc  (ec|aencia*  I.  Corpainia- 
f  Ce  nacura  ad  quietem  non  tendic ;  neqoe  magis  ad  qoie* 
tem  propendec,  quain  ad  mocum  ;  (ed  exigic  perleyera* 
re  in  eo  ftacu,  in  quo  eft. 

Ildo.  Motas  omnis  nactira  faa  cqnabilis  eft,  flc  redili- 
tieufi  \  quare  oc  corpus  in  Itnea  curva  incedat,  pluribua 
Vtribus  ureeacur,  necelTe  eft ;  cam  enim  linea  cnrva  xqui- 
Valeac  penpheris  polygopi  infinice  mulcorum  iacerum^ 
(ingula  aucem  lacera  aliam  diredionem  cxprimanc ,  opus 

cft  nova  continuo  direSione. 

> 

lilrio.  Corpasurcunque vaftnm  quacunque  direQione 
projedum,  fiirdim  five,  five  deorftim,  perpetuo  &  eadem 
celeritace  movcrecur,(i  cau(a  quspiam  excrinfeca  vel  dire* 
Aionem  illias,  vel  ceieritacem  non  immut»ret,ant  prorHia 
cxtinguerec*  Immutac  ftucem  fere  wdium  refifiens ,  uc 
in  corporibus  proje£tis  aSr ;  vel  fri&io,  dum  corpoaa  (u* 
pra  aliorum  corporum  (uperficies  lcabras  iocednnt  ; 
vel  gravitsSy  qu«  critur  ab  attrat^lione  c.  c.  terra?»  Uin 
dc  dam  cof pora  projcQa  per  medium  xefiftens ,  vel  peff 
•  A  a  .  %«• 


4  SeSiot  CaputL 

^pcrficiet  (cabras  defcf untnr ,  vel  vi  gravitatis  deoHam 
«rgentury  amictere  debent  eam  mocns  (ai  partem ,  qaam 
ibperandis  hisce  obftacolisjmpendant ;  &  amitterc  de- 
bent  boc  majorem,  quo  majus  fuerit  obflacnlumf 

Schol,  Dices  itno*  Motus  projcdorum  pauUtim  lan- 
gue(cit,  &  ipGi  mobilia  nltimo  ad  quietem  pcrvenkint; 
crgo  Tidentnr  corpora  mota  per  (e  ad  quietem  teilaere* 
J^  Langue(cit,  imo  extinguitur  fropter  tnedium  refijleus 
C*  A*  p^fit  ^'  A.  &C*  Sicut  corpus  non  poteft  figu- 
ftm  £emel  fibi  inda<3am  exuerc,  &  aliam  atfqtte  caufa 
txtrama  indnere :  fic  ncquc  motum,  ad  quem  icnfcl  de« 
tcrminatum  c& 

Dice§  ido.  Vi  lcgis  iftius  pofTet  lapls  fiib  mundi  prin* 
opiom  cjedos  u(quc  faodic  morcri  finc  uUa  motus  tm* 
tnotationc;  quod  incongrne  dtci  vidctcir«  ]$•  polTet,  fi 
motos  iu  vacuo,  (eu  (patiis  liberis  abfyue  gravitate  fieret. 
C.  A.  fecus,  N.  A.  &C.  Poflec  imo  etiam  in  tnedio 
^iquatettus  refiflente ,  fi  (ciiicct  lapis  omnino  ingcns  fo- 
rcfy  celeritas  magna,  &  mcdiom  cenuilfimum.  Sic  pb« 
Bctc  Q(qQC  bodic  motus  (uos  con(ervant,  qoia  movcncuc 
in  mcdto  rariifimo*  Certc  tcfte  KsiUio  matcria  illa 
omnis,  quar  tomm  Jpatium  plamtariitm  in^iet ,  fortajfi 
Don  adaeqoat  iliam,  qu2  i»  uno  digito  cuUco  noftri  aeris^ 

continctun 

Dices  $fio.  Corpus  nio(uni  cft  in  fiatu  violento  ;  at« 
qoi  nutlum  corpus  natura  (iia  exigit  per(evcrare  in  ilata 
violento;  crgo  nec  in  ftatu  motus.  ^.  N.  M.  Corpnc 
omnc  natura  fiia  iners  eft,  ac  propterea  indifferens  tam 
md  motom ,  qcum  ad  quietem. 

Dices  4to.  Corpus  omne  natura  (ua  indifferens  eft 
«d  motum,  &  quictcra ;  crgo  mobilc,  dum  movetur,  noa 
snagis  ad  continuandnm  motum  propendety  qnam  ad 
quietem ;  ac  proindc  natora  fua  non  exigit  perfeverare 
in  ftato  motos.  ]$•  D.  A.  eft  indifterens  hoc  (cn(u,quod 
fe  ipfum  ad  mutationem  ftatus  determinarc  non  poffit» 
C.  A.  tanquam  fi  remel  motum  deinceps  moveri  noa. 
Migat»  N.  A.  &  Q.    9«  *do  ^  indi^crcna  aiKc  dete# 

,   o)ina«  ^ 


} 


Leffi  mrtus.  ]f 

mtnationem  acl  motuni ,  vcl  quiet«m.  C  A.  faAt  detec« 
minarionc.  N.  A.  &  Cm.  Corpus  jtm  femci  dctcrmiqf» 
tum  cninbet  ftatus  fui  immutationi  rcfiftit;  nequcfnagit 
refiflit^  cum  tranfeundum  cfl;  a  quietc  ad  motum,  quam 
€um  a  motu  ad  qnietcm»  Arquc  cx  gcmina  hac  rcfiften* 
tia,  cctcris  paribus  utrinque  <tqt4ali,  conficitlir  indiffe* 
rcntia  corjioris  ad  motumi  vci  quietcm. 

§' ^*  LEXn.  Motus  fimper  eji  proJfcrihM^ 
Jis  caupe  aJieijuata  j  fiu,  ut  Neutonus  loquitur  ^  vi 
enatrici  imfrtft.  Pr;  Motus  efi  effeitus  flenus  vis 
mocricis  impref&s;  atqui  {perMtiol)  efFeAus 
pleni  funt  caiufis  fuis  proportionales ;  ergOt 

CoroU.L  Vis  igitur  dapla  duplum »  tripk  triplaai 
producec  cfFc£lum« 

CoroU»  IL  Ergo  eadem  cft^mennira  vis^qus  motos; 
h.  e.  Vis  zA  MC.  Nifi  fortc  iftud  intci^gcndom  fit 
dc  viribus  nicrc  mortutt^  non  de  vivfs,  Scd  de  hoc 
infra. 

CoroU.  Illi  Si  corpus  quicfccns  urgebitar  viribus 
gequalijbus,  (cd  /econdum  coutrarias  dircdioncs,  mancbic 
immotum  ;  cum  vircs  seqoaies  oppofitis  dirciUonibos 
agcnrcs  (e  elidant. 

CoroU.  IK  Si  Gorput  quiefccns  urgebitur  viribus 
fpeCtata  direfiionc  oppofitis,  &  iiiaqttalibus  ^  movcbitur 
(ecundnm  dircfiionem  vis  majoris  \  &  motus  proportio* 
siaiis  crit  differencic  viriuro. 

CoroU,  y*  Idem  {entichdum  de  corporibus  irNm^ta 
confiicotis»  fi  vialiil  five  stqp^li,  five  incquali  iiecQodani 
^cdioncm  oppofitam  orgcantur, 

ScboL  L  EffcSus  plcnos  cflc  caofis  fiiis  «qoales  (Te 
dcmonftrator ;  in  effedu  creato  non  poteft  cfle  plus , 

?uam  in  caufa  adsqnata ;  (ecus  eric  iUudplus  finc  caofii^ 
k  ratioqe  (ufficiente.      Nec  potcft  cfTc  tninur^  (ccos  fart 
Mlifua  ifirium  applietibitar  fine  cationc  (iifficicnte. 


6  SeSio  L  Caput  T^ 

ScboL  IL  NcDtonus  vim  tnnricetn  impreffam  dicit 
aSionein  in  corpas  exercitam  ad  mutandum  ejus  (Urum 
qniefcendi,  vel  movendi  uniformiter  in  dire£tnm  ;  quAm 
Vim  docec  conliflere  in  fola  «dione,  neque  pofl  adioncm 
permaner^  in  corporc,  cum  corpus  omticJu  oruui  fiatu 
n^vo  perfeveret  per  folaiiri  vim  inertiflt.  Addit :  vim 
lianc  diver&s  origines  haberc,  ut  ab  i£^o,  pi^flione,  vi 
centripeta.  Ex  advcr{b  "uim  iufitam  corporibas  nuncu» 
fitlpotefitiam  rejtftendi^  qua  corput  unamquodqi)e  per* 
leverarc  nititur  in  ftatu  Cuo. 

Sehol  UL  Dicesi  S«pe  vis*eft  percnignt,  effeftai 
ingens ;  fic  vis  rcintill^  uniuS)  qua  pulvis  pjriut  maiort 
copia  congefius  accenditur,  modica  efi,  fi  conferatur  cam 
cfTeilibus  ^  quos  in  cverfione  urbium  >  ant  munimento* 
fiiiti  experimtin  ^.  Vis  tgniculi  uniua  non  eft  cmijk 
adaquata  fa£lx  everfionis;  (cd  omnes  ignicult,  qai  priat 
in  puIveN  nitrato  nondum  aceen(b  certis  velut  repago* 
lis  adftri£li  detinebantur  ^  fubinde  eic  ergaftulis  fuis  eli* 
beraei  ftragem  illam  edunt  ^e  lu£(uofiim«  Hcc  caa& 
ad^quata  squipollet  cffc6iui  fuo  i  &  viciffima 

^.  4*  LEJC IIL  AHiom  e&ntraria  fetnfn^ 
tf  stfualis  efl  naclio.  Sive :  corporum  duoriim 
aAiones  in  fi  mutua  femper  funt  arauales»  &  iil 
partes  contrarias  diriguntur.  Pr.  imo.  dari  im 
corporibui  rea£lionem\  naecenim  nifi  detur,  po« 
teric  minimum  corpus  in  motu  pofitum  m4« 
Simo  tuique  quiefcenti  communicare  motuni 
fuum ;  non  dotem  poceft ;  ergo,  Plura  dabo^ 
Cum  de  inertia  agam,  Pr«  Ildo  oHioni  eontra* 
riam  ep  reaffionem  ;  nam  dum  corpus  ununi 
agit  in  aliud»  illud  ad  mocum  (blicitando  :  p3-« 
fiterius  priori  refiftic  vi  fu^inercia;  (  eilauceni 
inercia  aifiis  adverfus  agentis  ni/um    Ce  A  exe^ 

rtns)  I  de  vi  impelleouf  femper  aliquid  den 


^erpk;  partes  6jus  vi  fua  elaftica  CMipritriit ; 
(icque  comprimencio  in plagam  oppojitam  dirigi^. 
Pr.  Illria  4(fioni  ^quAlem  iffi  ndSliorum  :  cor- 
pus  non  reagit  in  aliu(}  e^  c.  impingens»  nili 
quatenus  iftu4  illius  flatuip  conatur  inimuta- 
re  i  erga  rea<^io  corpiQrisi  r«(iftentis  asqualis 
^&  a<5tioai  <;orporis  e.  c^  impingentis ,  fic  vi-* 
cinim  ;  aeqip<^  etiam  corpus  impingens  eatc- 
iius  ^2tc\Ct  agit  in  qg,iei^ens^  c^uateou^  hoc 
tpat^i  illius  re^ftit,, 

Srboly  I^  Si(  vis  equi  {apufcin  trafientis  ad  Tim  ejaa» 

^^in  lapidl$  mptioni  renft^ntis  ut.  toQ.  ad  ^o.     Dico  : 

equiis  iapidem  non  trahet  vi  ut;  ico  ^  fed  ut  50.     Re- 

.{idiia  viriiiim  partC;  progredietur  eum  laptdeyS&f  frfiu 

pem  qonjunBo^    Sic  legem  hanc  illuflrac  Cl.  P.  Htnr^ 

'  fauli^n,  S«  J.  ^   (icque  iUu(trand9,  verum  Neutoni  {ktt\ 
fym  expofuirti  Sb\  vi,detiir^ 

Scboh,  U^  ^e^utonus  ita  menteis,  (uaro  explicat :  Si 
corpui  afiquod  in  corpus,  ^liud  tmpingtns ,  motum  ejus  vi 
jiia  qiiomfidocunque  mutaverit^  id:  quoque  vicijjim  in  motu 

^  proprio  emdem^  mutationevj^  in^  partem  ^cntrariam  vi  aU 
^rius  (  ob  aqualitatem  prejj^iniu  vmtue^  )  Jitbibit.  His 
^Slionikus  aquahs:  funt  muiationes.  uon  velocitatum ,  Jed 
enotuum  ;^  fiilicet  iu  corporibus  non  aliunde  impeditir^ 
Mutationei  enim  velocitatum  in  contrarias  itidem  partes 
faB^  ^  quia.  motui  ^qualiter,  mutantur ,  funt  eorporibus 
froportionales.^  Notationem  merentur  voces  finguic  ; 
^x  cumpriiriis  ^  quibus.  veloQitatcm,  jntcr  »  &  motam 
4i^ernitur.        .     ' 

S^baf,,  IJIt  Ut:  omfiis:^tt0fUK0mbiguit€f  (inquiant 
C^ebervhniCvunmcntatores  inNeiitomimPP*  Jacqaicr, 
^  le  Seur  >  niiifl  atiud  por  kgemi^  banc  intelleOum  vobt" 
vmSf  nijt  ^fuales  fieri  iu  cotpore  agente,  ^  patienH  Jia*, 
mr  muiationes ;  atm  tnim  msUa  pojjtt  ejfe  eitio  oorporis 
m  ^iui  e^rfnf  ^  qfiin  msaua  fioM  horumce  corfHrum  coUi-' 

A  4  >&* 


8  Stffiol  CapHtt 

/to  i  fmHii&  flatust  ofuaiite^  in  utrofue  eorp^t^  ncift 
^iet;  uiuU  licet  ailhm  ^quahf  ftmf^rfit^  ^  coutiraria 
reaih^ ;  nm  idcirco  tarfktu  inter  corpttti  ngc^v  y  (^  fofitut 

.  fari  dehi  xqmlibriuni  \  idque  NeufOfuatto  wtnfk  tmiii* 
fe/ltm  efi  'k  fi  €^ii  iopidem  trabmtis  oonuttm  Hc.  itt 
riipra  iA  ancttj  QxcHr.ptoit  ScUicci  »nQn%>ra  vis  iinpciidi* 
tuf  ^  e<jiu>  ad  fiiperaodaiii  lapidis  refiftentiain  ;  Ad  cft 
duiKaxac  pars»  qi>2  refidenrfain  lapkiisftdaqiier»  tc  vt» 
luri  cHdat  /  reliq^a  adhibeiiciir  a'd  incedciidatn  five  w^ 
dim  ^  feo  ceievitis^      Qiiocirca  totaUm  eqni  a&iaucm^ 

^  in  gemiitas  partiales  diChibuere  llcec  :  alrerau3»(iua  Upida 
renft<ntiaj3i  CQlUt ;  altcraiti,  qua  progrediAtur.  Saia  illa 
prtar  squaKs  clirea£!ioni  lapidis,qaa  lapis  per  gravitateffk 
fuam^  ptani  fiairitiem^  ^  medii  reJt[tiH*iam  equQ  trahoo* 
ti  reliiQatar. 

ScbcJ.  I^.  IXice$  I.  Siiafiiani  contraria  {eoiper  «  & 
«qualis  efl;  rea^io,  nuUus  Ququam  exlftet  mocus.  '^  a€Ua 
cnim  impetlencis  elidccur  per  rea^tioaem  rcGftenrls  ;  ac^ 
proindc*     l^*   Si  a£Vioni  totali  retponctet  sq[ua|is  rea6>ta 

'  Ci  A.  St  parttah  N.  A.  &  C  per  readionem  non  eli* 
ditor^  niii  adiOy  u»  fic  dicam,  partMlis  tn  c«M*pore  agenre^ 
qw  rciKcet  impei>dirar  ad  fuperandatn  corporls  reu(ict> 
tiam.  E.  C.  Globus  ]>lumbetts  aqu«  immerfus  tantum 
ponderis  amictcre  viciemr»  miflntuin  ponderis  aqoa  habee 

flobo  itH  {pefbta  magtiituuine  rcQioncfens.  Quare  gIo« 
us  amifTo  iHo  pondere  refidemiana  aquae  tollit.  Rett* 
quis  fuis  viribns  fundnm  pecit* 

Dices  lldo.  Si  rea^lio  squarur  a£HofiI »  babenur 
atqualicas  momentorcim,  iive  a6tionum  ;  erga  agCBS  ^  & 
ipaciens  func  i.n  squilibrio  ;  atque  adeo  quTefeunt  \  (od 
lic  nullus  habecor  inocus;  ergo.     ^.  ut  fupra. 

t>ices  llltio.  Si  data^  lex  obrineft :  eiir  vitrom  inaU 
leo  ferreo  pcrcnfliim  frangitnr ,  non  maileijis  ?  cum  ta% 
inen  idus  sMjue  in  malleo  rectpiatBr ,  ac  in  ritre*  i^m 
cum  KeiUio  :  quia  ^ artes  ferri  duriores,  &  firmius  fiki 
cohcrentes  muho  fortius  eidem  percuflionis  virefiftuai^ 

qnam  partoi  viisi  admodiuii  fri^iks »  intfiiii^ue  eoboh 


^    V 


Legtf  motuu  9 

Dtm  lVt9.  At  raltem  ferient  «Itenim  c^ftlem  ipft 
dolorem  (enrtre  deberet ;  non  autem  (entit;  ergo.  l^. 
non  fentit,  ii  inftrumento  utaitur,  vcl  partibos  tnhm  fm* 
fitivis  feriat,  C  {eeo8,N.  Fac,  palmt  palmam ,  manu9 
mainim  qdatftt :  arqualis  otrinque  dolor  ( caetcris  pari« 
4)09  )  (entictur. 

Dices  Vto,  In  mutnis  attraftionibns  non  •bftnrstiir 
ioflionis,  Qc  Cea^lionis  squalttas.  $.  N.  A.  Si  iM^»sr 
imponatQr  fuberis  frufto  A ,  firrum  alteri  frufto  B  ,  6C 
cam  magneSy  ^uam  ferrom  aqux  innatet ;  raagnete  mt- 
siu  retento  accedet  ferrum  ;  retentoque  ferr o  accedet 
snagnes.  Si  utrumqne  iibere  aqo^  commicratnr ,  mutua 
ad  te  (e  accedent,  sqoaH  utrinque  motti^  licet  npn  «qua)i 
tckritate  (ni(i  forte  &  magneSi  &  ferrnm  ejusdhn&nt 
fonderis  )  •  sdo*  Si  quis  in  cymba  A  conftitutos  opo 
funis  verfus  (e  trahat  cymbam  alism  B ,  habcbinir  mii* 
tuus  eymbarum  aeceflosy  com  cqoali  quatait€te  metns  ^ 
&  6  cymbscpondere  =3  \t%  fuerint,  cum  ae^uali  eeleri^ 
tate»  3tio.  Si  quis  in  cymba  pofitus  funcm  littori  aDi* 
gatum  trah^t,  eaquc  Tatione  Utcus  ad  fe  pcrtrafacre  niti* 
tor  t  cymba  ad  litrus  accedet)  &  viciflun  littus  ad  cym* 
|>ain  €quali  mtu^  (ed  multom  inaquali  eeleritate  i  facc 
cnim  in  littore  (  cujus  magnitudo  adarqnat  reflduse  mo- 
lis  terrens  magnitudinem ,  utpote  cui  nrmiter  adhs^rct  ) 
cft  infinlte  parva;  ac  proinde  f{)cdari  poteft  ut  nulla;'!!- 
€ct  Geotnetriee  j  &  ad  rigoretn  loquendo  dicendom  litji 
quod  Itttus  ad  cymbam  accedat,  nonfccos»  ac  cerra  a4 
lapidem  cx  aito  dccidentem. 

Dices  Vlto.  Atqui  dam  lapis  jeciduus  terrani  pctif^ 
tcrra  viciflini  ad  lapidem  non  afliirgit ;  crgo.  ^«  non 
olTurgit  moto  ienfibili  C,  m.  inSniibili  N.  m.  &  C« 
In(enflbiHs  eft  motus  terrs  verflis  lapidem,  qnia  infinita 
parvus  cft ;  hinc  pro  aihilo  haberi,  totoque  js  Phyficis 
negligt  poteft,  Rem  flc  oftcndit  KeiUius  :  Si  iis,  qoi 
dimenSoncmterrc  fcnD&rfint|fides  faabcnda^tota  teiluris 
moles  eontinet  3o^ooa^ooot^ooo#ooO|Ooo  oeo  oo^ 
|Kd«i  «ob.  I  fiu  trie;efias  millc  triUionn  ^am  ci&icoq 


•tw 


«      « 


-10  Seflhl   Capui  If^ 

rwn,  Srqtic  ifticoinponatur  c*  c»  Upis  lo©*  pedo^ln  CH* 
f  lcoram  :  erit  tcUu*  ftoftr^  ad  diftvim  iapidcm  ,  ut  rr«,. 
cenri  triUioncs  ad  i,  Porro  lapis  illc  cx  alto  dekbcn^ 
fempore  minuti  nnius  (ecandi  decurrat  pcdcj  prope  fj^ 
(cotidem  CIU91  fere  rrihumtnr  corporihus  libere  dcfccni 
dcntibus)  i  ajo;  tcrra  vf  fT^wt^f^i^  <equalM  retroa&ionif  i^ 

15 


I   ^         n>.    !J  I 


Upideattraftadccurrct  30QQQ0  000  000  opo  000  ooq. 
nnius  pedis  co  tcmporq  ,^  quo  lapis  decurrct  pcdes.  15^ 
Kxc  vero  tantiiU  e(l  quantiras,  utipfam  im^gin^Qdi  vi(T\ 
effugtat, 

jNot($i  Hire^  &  id  genus  alia  qui  legis',  infantiai^^ 
prfltjudicisi dc|tonas,  opovccU    Sic  ^licjuandq  fipics. 

Caput IL 

Qusc  virium  Lex  in  naturs^ 

cxiftat, 

S.  J,  Corpora  frcijuentibufy  tf  quotidianis  mu^ 
tationilus  funt  obnoxia.  Ligna,  telas ,  ofla ,  char« 
tae  &c*  abeunt  in  cineres,  Cinercs^arenjr,  & 
falia  in  vitrum«  Nitruni,  fulphur^  &  carboncs 
in  pulverem  pyrium,  Vitnolum  &  fulphw 
in  terrum  &c,  Breviflime  ;  Corpora  omnia 
moventur,-  ac  proinde  mutantur  j  atque  pra 
diverfitate  motuum  jam  cflentialiter,  jam  acci* 
denralitermutantur,  Porro  mutationU  hujus  r4* 
ff0yf(^i#»i  haberi  debet  (perMetapb.)  ^  quac  vii 
dicitun     Mutatio  cr^o  omnis  vi  eficitttr^ 

$.  4»  Hiverjie  mutatioiui  Jiverfat  fibi  vires  de* 

fofcum\  fifl^ulx  cni^  mutationcs  ruambabert 

dc? 


Ltx  virtum^  I  \ 

^       debent  rationera  fufficientem,    Neque  fup v , 
bac   virium    diYcrfirate   litem  movent    fanc 
•  'mentis  Philofophu     Iftud  jam  affidup  qua^ri- 
tur  :   ^ua  in   rerum  Inatura  hx  virium  ^cncralif 
€^sjlai.    Exiftere  autem  puto  fequencem  t 

Lex  yirium  generalis. 

^,7*  y^^csinHhimis/liftantHtfiwpmrfintrgpul'» 
Jtva^  mutua^  cuivis  vclocitati  Mingucndd  farcs^  im^ 
cninusis  in  infinitum  diftantiis  crcfccntcs  in  infinu 
tum^  auRis  dccrcfccntcs  >  ac  in  quadam  diftantia  ad^ 
modum  cocigua  ctiam  cvancfccntcs.  AuBa  pauUulum 
difiantia  abcunt  in  attraftivas  crcfcentcs  frimum , 
mvx  decrcfccntrs  y  dum  cvancfcant.  Iftis  itcrum^ 
fariquc  incrcmento  primum ,  tum  dccrcmcnta  fuccc* 
dunt  vircs  repulfiv^ ;  qua  attraSlionis  9  ac  rcpulfia^ 
nis  altermtia  obtinct  in  phrimis  difiantiis^  fimpcr 
tamcn  adhuc  mimmis.  SuUndt  in  majoribus  diftantiii 
vircs  fcmpcr  funt  dttrailiv4C ,  agentcs  ad  fiyum  im 
rationc  invcrfa  duplicat4  difiantiarum.  Hxc  c(l 
tiaturs  lex  a  Cl,  Viro  ,  ac  magno  Geometra 
Rogcrio  Bosc&vicb  S«  J,  feliciter  in v^nta ,  &  no« 
biscum  in  Pfailorophiat  naturalis  theoria  N«ZO« 
iisdem  prope  verbis  communicata. 

Scboh  Ifta  virinm  niiitiiarutn  tbcoris  (  qntm  con*  ■ 
t\mo  ciberiiis  exponain  )  diffcrt  a  tbe^ria  Neutoni ; 
•tque  in  CQ  djfFcrt  potiiTtmQm ,  quod  Neutenus  in  mi* 
nimif  diffaintiis  viret  tdmittat  po/ttivar^  five  attraSivas  t 
Mofifr  iilc  ucgativas^  h,  e.  r^lfivas\  unde  contaBum 
immetionnn  ,  (i?e  (  nt  eum  •ppell«re  folet )  AUtbema,  ^ 
ticum  a  pun£(is,  &  qMteria  omttine  esccludlt,  Tqih 
in  jlbeoria  gravitatif  Ncutonianse  aulU  babctur  mutati^ 


A 


12  Sc£li&r.  CaputlT. 

c  pofitiro  &i  negativiim,  ab  attraftiont  in  repnKionem ; 
#el  vice  verfi  ?  hnbetur  in  noftra.  Sed  ad  demon- 
ftrandam  legem  me  accingo. 

,^.  8.  Dejinitio  L  AttraSKo  eft  determi- 
Datio,  quam  habent  corpora,  aut  particuls 
inateriaei  ut  ad  (e  invicem  tendant  certa  lege. 

Seboh  I.  £adem  notio  {iibeft  vi  cemrifetd^  aat 
{iecileratrid. 

Schol,  II.  Corpora  quidem  omnta ,  minimaque 
ma^eris  pnnfla  &  &  mutuo  attrahnnt,  &  ad  le  accedere 
nitiintar ;  ut  infra  dicemus.  Dum  tamen  e.  c.  Corpus 
B  accedit  ad  A,  non  accedir  ratione  attra&ienis  pro- 
fxix  ;  (ed  olitnx^  reiidentis  in  corpore  A* 

§'  9.  Definitio  Ih  RepuJfid  eft  determina^ 
tio  ad  fugami  five  receflum.  Sic  corporibua 
oleoiis^  aut  pinguibus  non  adha?ret  aqua  ;  da- 
tur  itaque  in  oleo,  gut  pinguedine.vis  repulii^ 
yuj  id  eft  determioans  ad  receflum. 

^.  10.  Lemma  L  Corporum  eUmma  fufH 
ifitia  fimplicia  ;  nam  in  refolutione  corporuin 
tiltimo  perveniri  debet  ad  entia  (ynplicia ;  (e- 
cus  admittendus  eft  proceflus  in  infinitum  , 
quem  implicaro  docent  Metaphyitci. 

Corott.L  yitomos  fiamra  dicimus,  qas  licet  axten* 
lione  careant ,  {iiis  tamen  prarditae  funt  qualitatibos  i 
quaro  entia  fimpUcia  funt  atomi  natur^» 

SeboL  1$  Entia  fimptioia  Cint  corporum  elementa  » 
{ive  principia  pn^io,  vei  lihima,  mediata,  &  infittfihilia  % 
ita  Metaphyficl.  Phyfici  qncrere  Iblent,  qua  fint  Cbr- 
forum  mixtorum  frificifia  pfyfica,  (en(ibilia,&  (i  dicere 
licet,  elementa ,  aut  principia  fictmda*     Occidapi  ^va^ 

tlioncmi  (cd  prlns  ^iutpiam  adaotaboj 


Lex  vMum.  I3 

SchcU  II.  hefinitiQ  f.  Corpus  mixtum  cft,  quod 
conftat  particulis  hnerogemK  ,  (eu  diverlbrum  mifcibif 
lium,  certa  4|uadam  ratione  fibi  unitis.  Sic  fere  TfaUm- 
migius  cx  Wvlffio*  Corpora  mixta  (unt  animalia ,  vc« 
gctabilia,  fbiTiIia,  &  ii  quar  funt  alla. 

Schol.  IIL  Definitio  11.  Principium  feiundiim  funt 
illc  moleculs  (enfibilcs,  in  guas  ultimo  C  ^ilicct  adfai^ 
fitm^  quod  probc  notari  veiim  )  rcibivitur  mixtum  Cor^ 
ftn,  Moieculs  ilbe  alitcr  corpufiula  primitiva  nomi- 
nantufe!  propterea,  quod  immediatc  in  clemcnta  tqCoU 
vantur,  li  quibus  vtribus  refoivuntur. 

Corott  IL  Ergo  ficut  principia/^rifTM  corporisnon 
poiTunt  cfle  corpus  ,  fic  planc  principia  ficitnda  roixti 
corporis  cflfc  ncqucttnt  corpus  mixtum  ;  quapropter  he^ 
terogetteif  particuiis  conftarc ,  inque  eas  rcCalvi  non  de- 
bcnt. 

Scb^L  IV,  Non  ago  contra  Hejiodum ,  qui  (blant 
getram  ;  noii  contra  TiaJetem  Milefium^  qui  fblam 
equam ;  non  oontra  Auaximetiem ,  qui  fbium  aifrem  ; 
non  contra  Heraclidem  ^  qui  (blum  ignem  ;  non  contra 
ineptum  iliud  j4ichimiftarum  gcnus,  qui  Jpiritum,  nc(cio 
qucm,  univerfilem,  fen  mutuli^  per  totum  univerfitm  dif- 
fufuntj  rerum,  ut  ajunt,  caufam ,  prout  in  diverfis  meati-- 
itis,  ac  matricibus  receptus  fnerit,  mixtorum  principia  «C 
&  vplucrunt.  Tsdct  iftos  rcfcllcrc.  Rcs  brevicula 
laibicft  cum  iis  Chemicis ,  qui  principia  (cnfibilia  mix* 
torum  (^tuunt  quinqucs  l.Spiritum  (  aliter  il£rrcttr/«f;t, 
vocant  )  quem  Lemeryus  ait  cffc  part^  (ubtiiiorem , 
pcnctrantcm,  movcri,  &  movcrc  apriflimam  y  pro  cujus 
varia  aQivitatc,  &  copia ,  facilius  mixta,cre(cunt  ,  aut 
tarditts;  corruiiipuntur  imo,  ti  nimia  fuerit.  II.  Sul* 
fburf  fivc  oleum,  partem  corporis  inflammabflctn  9  dul« 
€cm>  pingucm/ &,  fi  poros  mixti  oppleat,  acornipnon^ 
prc&rvantcm.  II L  Sal,  (cu  ccrpus,  quod ,  teflc  fiocrha* 
vio,  aqua  potefl  dilui^  igne  aurem  fundt  ,  fi  non  avolaf 
frius  iu  auraSf  quodqut  guftum  humanum  afficere  valet  eo 
Jinfis,  qftern  faforem  apj^eUauu    Atque  bsc  trin  princL^ 


Ii^  ScSioI.  CaputlT. 

Mcrcoriiim  in  Btrometro  «que  actollunt ,  ae  aer,    ijf. 
Be  boc  phdenoineno  alibi  commoclius  agcttir, 

VL  Aer  diftingnitt^r  d  corpor^  mixro  5  ergo  tioxi 
poteftefle  priiicipium  mixti.  Ify*  Diflinguttttr  in  pars 
a  m^,  icu,  ut  phraii  fcholadica  utar)  diltinguitur  iuada» 
quatt  CX  A»  id^fquat^  N.  A^  &  C. 

VIL  Aer  permeat  omnia  corpora ,  ergo  non  eft 
pdncipium  corporis  mixtt.  P*  C.  Ignis  pervadens  fer^ 
rnm  ^  aqtia  (pongiain  ^  lox  vitruin  ^  non  funt  ekmenta 
ferri,  (pongi^iaot  vltri>  ergo  a  pari.  Vji.  C.  A.  D*Cs» 
trgo  atr  m»rUkks  non  eft  principium  mixti  C«  C« 
aer  corpori  propriuSy  qui  moteculas  mixti  cum  aliis  par« 
ticulis  eiememaribus  conftituit  N.  C     - 

VIIL  Non  omrita  mtxta  refblvi  pdfliim  in  minima 
elemehtari» ;  ergo.  Pn  A.  Aurum  haf^cnus  in  terram^ 
aerem)  aut  aquam  {blutum  non  eft.  Nec  aqua  !n  ferro 
tandente,  nec  ignis  in  glacie  latere  videtur.  ^.  D.  A* 
tion  omnia  mixta  6c  refolvi  pofiVint  immtdiate  &  pro* 
xime  C.  A*  mediate  Suhd.  non  in  omnia  quatuor  elemeil* 
fa  G.  A»  non  inaliqua  R  A*  &C.  Aurum  ha^enua 
in  elementa  {blutum  tion  eft,  defeAu  (cilicet  notitiar^ 
tnenftruijVei  inftrumentortim,  non  defet>u  natiVi»  con* 
ilitutionis  fuat.  Aqua  non  latet  ui  ferro  candente  ^ 
quid  poftea  ?  Non  atfirmo  in  ointiibus  corporibus  om- 
tiia  eiementa  contineri.  At  ignem  non  baberi  in  glacit 
prorfus  nego ,  cum  ope  machnide  eledlries  ex  ea  proli'* 
ciatur.  ^  ^ 

IX;  Mixta  revera  non  (blvuntur  in  minitna  ek^ 
mentaria  ;  crgo»  Pr.  A.  Minima^  li«c  elementaria  tui* 
icnntur  in  ipu  refohulone.  jgt»  temerd  iftud  aflerituf» 
C9%f'quidem  poflunt  molecnl;)?  elemcntares  difperfir  ^ 
atnon |[mr4ri;  quomodo  enim.? 

X.  Licet  mixta  folvantur  in  moleculas  elementa* 
res,  non  tamen  ea  dtci  poflunt  princij»ia  mixtOrum ; 
crgo.  Pr*A.  Etiam  cincres  plantaruin  folvuntur  irt 
partituias  quatpiam  ni^rieantes ,  ferri  fimiles,  Magnett 
adhmntes^  tiltrtnoQ  rolublleti  f uid  propnrea  «udiant 

priti* 


*  pjrinclpu  planumm  \  ergo  g  pari.  ^,  ut  ftpta  :  noiii 
fnnt  folubiles,  quia  moduscas  folvcndi  ignorattir ,.  flC^ 
apta  open  huic  inftramcnta  dcficiunt  C»  A.  cx  ft  N  .A. 
Sl  Q^  molcculas  i(hs  elementis  confiare  fuadct  analogia 
dcfumpta  a  corporibus  aliis,  imo  &  fcrro  communi. 
^  ^  XL  £x  aqua  iiafcuntur  animalia,  vcgctabilia,  fofll*. 
lia  ;  ergo  fbla  aqua  cft  principium  mixtorumt  P.  j4* 
iii  agua  reperiuntiir  minima  animaicula,  quoT)  ni(^  ocalo 
armato ,  e.»nfpi£i  non  pollint.  iL  omnia  anioialiurn 
ofTa  prir^cipio  moUia  funt ;  proinde  exaqua  ficrividen* 

'  tur.  III.  Hetmontm  BruxelUnfis  non  ceUbrif  rnagis  ^ 
fUflm  obfcurvs  Chejmcus^  ^  Akhimifta  (  verba  fiint 
^herfferi  )  argumentum  attulit  fahcem  51  Librarutn  ^ 
ducentis  tibris  terra  ^  ex  ^ua  frius  falem  extraxit^  im* 
flantatam ,  quie  fion  computatis  foUis  annttatim  deciduif 
164,  Libroi  appendehat ;  cum  interca  tarra  illa  (bla  aqua 
irrigata  dc  libris  duccntis  (blum  duas  amiferit ;  crgO* 
^.  N«  A.  ad  Prob.  Imam  dico  :  animalcula  in  aquis  re« 
perta  nafcunnirek  feminibus.  /tt  inquies:  ip(a  ad^o  femi* 
na  funt  Huida ;  ero;o  aqpca  funt«  Reddam  egp  t  ergo  ^ereay 
flammea,  ignea  uint,  cum  acr,  ignis,  fiamma,  fluida 
iint.  Vei  dicam  (emiil^  fieri  ex  aqjcia  tanquam  princi« 
pio  non  uuico  C.  C.  tanqtiam  principio  »»iroN.C.  E^- 
*  dem  refponfiQne  nteris,  ii  dicatur ;  Lapides,  Metalla,  & 
Fodilia  omnia^cK  aquis  nafci.  Quod  Udo  loco  oggeri* 
tur,  cadem  ratione  expcdies.  Ad  III.  ]}2.  Salix  ilia  aC 
furrexit  ex  aqua,  bcne  multis  particulii  hiterogeneis  ^ 
terrcis  ncmpc,  fulphureis,  mercurialibus  &c.  permixti^ 
quam  tdcirco  non  pttram  dicimus.  Quid  quod  etiam 
particulf  aereae ,  &  calorifers  faiici  incrcmentum  dare 
poterant.  ^ 

XII.  Moleculat  elementares  ip&  funt  eompoCtr; 
ergo  ncqueunt  effc  principia  comppiitorum.  Pr.  C. 
principia  corporum  nequeunt  efTe  compofita,  (ed  indifi* 
ferentia  (iiit,  oportet,  ad  corporis  cujnscunque  compoii-» 
tionem  ;  atqui;  ergo.  VfL*  D.  A.  Cint  compofits  cx 
cntibus  fimpliGibus   C.  A*    ex  p^tficulis   heterogenei^ 

B  N.A/ 


ig  SeSioT.  Caputll. 

N  A.  D.  C%.  ergo  nequeunt  clTe  prima  principia  com^ 
pofitorum  ,  vcl  nequeunt  cfTc  principfa  compofirornqiy 
quatenus  torpora  (luit  C*  C.  quatcnus  mixta  funt  N.  C4 
hlc  non  ago  nifi  de  mixtorum  principiis  fecundis* 

XIII*  Minima  elementarla  (ibi  mutuo  adverfantur; 
litignisaqus  y  ergot  i^.  adverfantur  (ibi  non  debite 
tttemperata  C.  A.  at^cmpcrata  N.  A.  6c  Cm. 

XIV.  £x  qualitatibus  molecuiarura  elementarioni 
fion  pofTunt  intelligi  qualitates  mixtorum ,  e.  c.  magnc* 
tifi  ;  crgo,  l^  ex  qualitatibus  fcordim  (pe£latis  C.  A. 
compofitis  N.  A.  &  &.  pro  diverfa  particularum  mint« 
marum  compoiitione  refiiltant  diverfse  vircs  in  mixtis. 
Sed  iila  fufficianti  qux  nifi  e^rcitationis  (cholailica  cau* 
fk  attuIifTcm^  nun(](ttam  allaturus  eram.. 

^.11.  Lemtna  IL  Omnc  corpui  foliJitat$ 
Jisa  cxcludit  ahcrum  dc  loco ,  qucm  occupat.     Veri-* 

tatem  hanc  quondianaexperiennafatisedoce-* 
mur. 

y.  12.  Lemma  III  CcJcritas  fnohU^pcrfaU 
tufn  mutari  ncquit  »  ita^ut  e  gradu  dctcrminat^ 
tranfcat  ad  alium  j  non  tranfcundo  pcr  omncs  graduf 
intcrmcdiou  En  fundam^ntum  (Vftcniatis  Bos^ 
£ovicbiani.  Pr.  Fcratur  cnim  moUU  ccrto  aliquo 
iontinuo  tcmporc  cclcritatc  1 2  ,  tum  momcnto  aliqu^ 
tranfcat  pcr  faltum  ad  cclcritatcm  9 ;  altcrutrum  ab^ 
furdum  confcquitur  :  vcl  dupkx  codcm  individuo  mO'^ 
mcnto  hahctur  cclcritas^  nimirum  IS.C^^,;  vcl 
ftuUa  tcmporc  aliquo  continuo  cclcritas ,  adcoquc  mom 
tus  interruptio;  cum  enim  momcntum  iUud^  qu0 
fakut  ficri  concipitur ,  Jit  limcs  tcmporis  antcccdentis 
Sf  conjcqumtis  »  codcm  iUo  momcnto  hahcri  dcbct 
€cUritas  antMdcm  |    £5'  confcqucns ,  fcu  cclcrita» 


Lex  virium.  19 

1 2,  £/  9.  i  quod  impUcau  Aut  vero :  /  aJiud^Jl 
ntomtntum  ,  ^m6  habetur  cekritas  ultima  1 2  ,  aliud 
guo  babetur  celcritas  prima  9  ,  cum  inter  bina  illa 
ntomenta  necejfario  interjaieat  tempus  continuum ,  in 
^o  momenta  funt  infinita  ,  tempore  ifto  intermedio 
fnohile  carebit  omni  celeritate*  Ita  ex  Boscovichio 
Paulue  Mako  Soc.  J£su. 

^.  15«  Pofitio  ad  demonftrationem  pravia  t 
Hantur  in  torporibus  vires  attraSiiva ,  if  repulfiva  9 
de  qiiibus  tanicn,  num  intrinfecae  fint,  an  ex- 
tnnCecx  »  nihil  difputo  ;  five  :  an  ex  ipfa  ma^ 
uria  Miur^  dimanenc ,  quas  pro  ratione  diftan- 
tiarum  jetigat  jam.  accefTum  ,  jam  receflum  ; 
an  a  lihera  DEI  legc  pendeant ;  an  ab  ali^uo  ter» 
tio  iis  adjeSio  (  quodcunque  iflud  fit)  non  qua?- 
ro;  nec  vero  ,  fi  veiim  qu^erere  ,  inveniendi 
fpem  habeoy  ait  Noder  ille  Boscovichius  \  adeo 
nacuram  rerum  intime  perfpicere  intelledui 
humano  concefibm  non  eft.  Pr.  Pofitio  :  £x« 
perieotia  conftat ,  quod  corpora  fefe  mutuo 
aurahant ,  &  repellant;  attra<^io  illa,  vel  re^ 
pulfio  nequit  haberi  fine  vi  (  cum  nihil  fiac 
fine  ratione  flifiiciente  )  ;  vis  autem  efl  ratio 
fufficiens  adionis ;  ergo  dantur  in  corporibus 
vires  attra^aiv»,  &  repulfiva?.  Pr.  M,  expc- 
rimento  a  CL  P,  £miVr  Ord,  Orat.  inflituto» 
&  in  adis  Acad.  Parifl  ad  A.  175 1.  defcriptoi. 
Div^rfas  ilie  materias ,  ut  papyrum  ,  corium» 
lignum,  ferrum  adaptavit  in  formafn  acuum 
niagiieticarum  tenuiilimarum ,  unum  ferc  pe- 
dem  longarum»  Quibus  e  crine  fufpcnfis 
dum  diverfa  alia  corpora ,  qusc  forte  pr«  m^^ 

B  2  nibus 


; 


29  SeSi^  l  Caput  TT. 

tiitm  eratit ,  admovit  in  diftantia  duaram,  vel 
trium  linearum  ab  extreiiiitate  ac^um  iila- 
rum  :  omnes  >  nulla  excepta  »  quinque  vel 
fex  minutis  fecundis  a  fa(5ia  admottane  ela^* 
pfis  ,  partim  attraAae ,  partim  repuiif^  funr. 
2do«  Eademattra<5i:io,&repu!nohabebatur  per- 
inde  in  vacuo.  ^tio*  Vitro  interpofito  attra-. 
£t\o  imminuta  quidem  fuit ,  at  non  omnino 
fublata  4to.  Subinde  flamma  admota  acus 
omnes  celerrime  accefTerunr;  etiam  ferrea  \U 
la  9  antea  femper  nlinus  ad  motum  prompta. 

§  14.  Pr.  eadem  M.  per  partes,  ac  primnm 
Jita  corporibus  atfraliio  vindicaturphanomenisfane  ma^ 
nifeftis  :  L  Gutt^e  fluidorum  figuram  fphaert- 
cam  alFumunt  ,  excepta  ea  parte,  qua  folidis 
adhsrent,  irel  incumbunt.  Si  gutca  e.  c.  aquas 
juxta  aliam  ponatur,  coibunt  ambae  in  unam, 
^i  Alcohol  vint  fpiritui  urinae  admifceatur, 
fere  momento  oritur  foiidum  afiine  glacici ; 
ir^o  datur  miitua  ftuidorum  attralfi^.  Ildo.  St 
fluida  quasvis  in  modica  quantitate  capiantur, 
adbasrent  folidis  prope  omnibus;  fac  enim  > 
mitte  in  aquam  digitum  ,  lapidem»  meralla, 
papyrum,  &  alia,  qa«  voles,  corpora,  (mo* 
do  lie  oleo  »  aut  pinguedine  fint  illira  )  ad- 
hasrefcet  aqua.  Si  corpus  fluido  immerfum 
cxtrahltur,  alias  fluidi  moleculas  prope  fuper- 
ficiem  elevat  ^  alias  fecum  abripir.  Plantae 
aquis  irrigarae  easdem  attrahunt.  Si  fruftum 
panis ,  vel  facchari ,  aut  falis  indurati ,  una 
fui  extremitate  fluido  immergatur  1  aCcendec 
fiotdum  ultra  libellam  non  fecus^  ac  in  tubis 

capil-  - 


^ 


capillaribaf,    Pix,  febum,  cerj,  o!euin»  Src* 

ineliychnio  afcendune,  &  fl^mmat  pabufUm 

miniltranr,       Mercurii  gixttgi  fiunno    afFu(a  in 

fpharrulam  fe  fe  non  comporflti   fed  quaqua-* 

verfum  difFunditur  ;  cum  interea /irra,,  ^^gw^t 

aut  cbarta  afiufa  fph^ricam  figuram   induat. 

Si  Mercurio  flanni  fruftum  immergatur,   ap 

furget  Mercurius  circdm  fuperficiem  corporis 

imn^erfi;  at  imnierfb^ferri  frufto  deprimctur, 

Caviraribus  ac  faveolis  circa  ferrum  rciidiis  ; 

irgo  fluida  a  folidis  attrahuntur.      Illtio.   Si  cor- 

pori  fluldo,  &  Vifcofo  committatur  aliud  Co\U 

dum )  adeo  fortiter  adh^erebit ,  ut  vi  f^epe  non 

niodica  opus  fit  ad  illiid  avellendum  ;  proindc 

etiiim  folida  a  fiuidis  attrahuntur.     1  Vto,  Magnes 

fequitur  ferrum ,  mercurius  aurum ,  &  vicif^ 

£ni.     Corporibus  eciam  lubricis  guocutxque 

Ctu  locatis  ,adh«rent  pulvifculi,     Vitra  ,  mar- 

inora,  metalla,  &  corpora  pleraque  laevigata^ 

fibique  intrita  adhaerent,  &  hoc  fortius  ad- 

haerent ,  quo  magis  fucrint  expolita.     Ccle- 

bre  efl  illud  Mufchpnbroeckii  experimentumx 

accepit  geminc^  cylindros,  bafibus  benepoH- 

tis  (  quarum  Diameter  unius  erat  poUicisRhe- 

nani ,   &  ii.  linearum)  &  fuperne  annulis 

firmis  inflru^ftos ,  c]uos  dum  ficcos  commifit, 

feu  :  alterum  alteri  appreifit,  cohacrebant  ut. 

cunque  firmicer.    CalefaAi ,  feboque  inundi, 

tum  reftigerati ,  nifi  appenfis  298  libris  nq^i 

fejungebantur.    Pice  illiti  850  libras  requir^- 

bant  j|d  fui  avulfionem.    Au^^bafium  dlame* 

tro^  dum  nempe  evaderet  digitorum  ji^arumg 

JB  3  ^ 


22  SeBio  f,  CaputlL 

&7  line^runii  (eboque  inunAi  cylindri  mar^ 
niorci  coharebant  vi  1 1 50  librarum^  JBrgo  iS^, 
wutuA  folidorum  atfraStio  efi  admittenda^ 

ScboL  Sed  nihil  mutiiam  foiidorum  attra6lionem 
sque  prebat ,  ae  operationes  chemicx ,  de  quibus  ini 
.fra  ;  tum  qviaevis  corpora  ,  quac  fenfibus  noflris  ^dibji- 
ctumur.  In  his  molecula  molecul^  adhsret,  &  validit^ 
fime  quidem  in  corporibus  duris;  non  ita  in  moilibus. 
Cur  vero  ^  fi  non  propter*  attra£lionem*  Nifi  detur, 
«ttraSio  y  nulla  dabitur  molecularum  cohsfio ,  nuliain 
fxtenjum.    Sed  etiam  de  hoc  alibi  dicendi  locus^  erit. 

§,  1 5  •  Etiam  vis  repuljiva  eorporihus  eft  tri* 
luenda.  Aqua  corporibus  oleofis,  aut  pingui- 
bus  non  adbaeret,  Sic  bleum  »  &  aqua  non 
commifcentur,  nifi  diutiffime  agitata ;  cefTan- 
te  imo  agitatibne  rurfum  feparantur,  *  Tela 
cerata  aquam  non  admittit  ; '  binc  ea  utimur 
ddres  a  pluviis  cu(lodiendas«  Animaliuni 
quorundam  penha?  non  madefiunt,  licet  per- 
petuo  fiib  aquis  delitefcere  videantur.  Lin« 
teum  aquas  tranfitum  nonnegat;  negabit  au- 
tem ,  fi  femine  Lycopodii  obducetur.  Suber, 
porofiflimum  corpus,  nec  vinum  tranfinittit, 
nec  aquam*  Si  aquas  fiagnanti  oleum  afFun- 
das ,  olepque  fiiperinfufo  guttam  olei  Tere» 
binthini :  circularis  repulfio  orietur  miram  re« 
ferens  colorum  pulcherrimorum  varietatem* 
Si  xt\  liquato  aqua  infundatur  ,  tam  vqhe* 
tfsens ,  ac  repentina  orietur  ^dio  aquas ,  ut 
omnia  fiimmo  periculo  disjiciat ;  cum  fnterea 
aurum »  vel  argentum  liquatHm  aquas  infufum 

folum  In  grduiila  abeac  cum  ali^uo  flridore« 


\ 
\ 


-> 


♦ 


Le^  viriuM»  dg 

En  vim  repuinvam  aqiix »  qu^  tamen  zri^^ru 
gido  adhaerere  prompta  eft.  Aer  in  fclopo 
pneumacico  coardarus ,  folutis  tandem  repa« 
gulis  magna  yi  ejicit  giandem  plumbeam. 
Si  ela(lrum  quoddam  cbalybeum  Tfig.  ima. ) 
dppreheniis  extremis'  A  &  B  primum  diduca*'» 
liir  )  ceflante  vi  extendente  continuo  priori 
fe  (e  feftituet  Otui  ,  particuiis  fciiicec  (e  mu- 
tuo  attrahentibus ;  fi  vero  eladrum  idem  com» 
primatur  ,  definent^  vi  comprimcnte  iterum 
In  priorem  fitum  abibit ,  fed  paVticulis  (e  fp 
mutuo  repellentibus»  Denique  omnia  corpo- 
ra  elaftica  comprefla^  vel  inSexa  »  ac  libi  fub* 
inde  relidta  figuram  priorem  Tuapte  recupe- 
rant.  Qua  cau(a  f  profe^o  non  alia  ,  quam 
quod  ex.  c.  corporum  infi^xorum  particulae 
ex  parte  convexa  mutuo  fe  attrahant ,  &  ex 
p^rte  concava  repellant ;   ergo,  ' 

StM,  Sed  nihil  iterum  inutuann  repuKionem  scque 
probat)  aC)  quae  quotidic  imucmur  5  corpora.  Nifi  cor- 
porum  nlolecui£  minimx  in  ulcimis  diiUntiis  (e  repeU 
lerent ,  compenecrarencur  \  ac  proinde  hoc  ipfb  nullum 
iSaretur  corpus  ektenfum  ^rgo  ex  obviis  quibusque 
corporibus  &  attra£lio  probari  poteft^  &  vepuliio» 

'^*  1 6.  Si  in  corporihus  >  ttiam  in  punHi$  eJc» 
mcnuribui^  five  entibus  fimplicibus  >  dAri,  de* 
Itnt  vires  attraSliva  \  if  repuljtva.  Pr.  Corpo- 
ribus  nulla  vis  inefie  poteft,  nifi  qoatenus  ea 
ex  viribus  elementorum  coalefisit ;  ergo  fi  cor- 
poribus^:  etiam  pundis  elementaribus  vlres 
attradiva?,  &  repulfivae  inefl^e  debent.  Pn  A. 
Vis  omnis  {.ferCefmgL)  ineit  fubftantic  j   in 

B  ^  ^        cor- 


S4  SeBio  h  Caput  TT^ 

co^oribus    aurem   nihil    habetur    fubftantiae 
praefcr  pun(Jta  elementaria  ;  ergo* 

ScbQll  X-  Nifi  piuuU  cUmQnraria  ft  ft  in  certis  dt- 
ftantiis  atrrahartr ,  fcpfuiHTi  jiui^clQ  non  cGnjnngentur  ^ 
jiequQ  unum  qui^  effiqient.  Nifi  in  certis  oiftantiis; 
£p  repcWaiw,  compcnetrabunturj  ac  prbinde  nullum  ui*- 
qiuni  habcbitur  ^xtenrum*  Hec  c(l  >  q^uod  proximU 
duobia&  Scboliis.  in&nuavi. 

Sc/joJ,  Ih  Fk)jc  Joco  propriet£^tes  ^  &  kges  attra3io* 
nis  no4)  cxamiuo^  Unuiu  aflud  contcDdo :  dari  in  na<« 
tura  mo<us  ,  quibus  corpara  ad  ft.  ft  mutuo  accedunt  j 
qui  cx  nullis  prrncipiLs  Mechanicis  y  non  cx  preffionc  > 
6£  iinpulfionefifc  acris,  fiveaetheris,  non  ex  corporum^ 
aut  nsekcularuai  figT^fi  a  dcduci  pofTunt ;  qui  a  viribust 
©I  dinariis  pi*ofici(ci  necja.ieuni  ;  qui  per  diilinSam  quan-- 
dari9  vl:n  (  quam  cufaNeurono  attrahentera  dicerc  li^bet ) 
explicari  debcnt»  Singula  Schalio  ftqucmc  raanilefis^ 
dabo* 

•  N, 

SchoL  IIL  Adverfuni  vircs  attraftivas  ©bjki  fclenfr 
fcquentia  :  Imo.  Pba?nomena  pro  artrailione  alUca  noa 
evineunt  atrrailionem  dagi  five  \n  corporibus ,  five  iix 
elcmentis  j  crgo.  Pr.  A  Qiiod  gurtc  omniura  fliiido^ 
rum  figuram  fplisericam  induant  ;.  c^od  cyliudii  dua 
fcenc  politi  firmirer  fibl  adbicreant ;  quod  molcculae  mi* 
iiiinab  corpora  conffituentes  adco  Valide  coniungaxituc 
&c.  repcti  potett  a  fluido  atiquD  cxtripftcus  premcnte  > 
iive  ab  aerc  incumbcnte,  Cc  pro  rationc  bafis  Tivc  (  quod 
ftuidorura  omniura  eandem  altitudinem  habcniiuin 
proprimn  eft)  pf-emcntc  ;  ha  Cartcfiani.  ergo.  Iji^ 
N.  A,  adPr.  N.  A.  Singula  cnim  haBC  phsrnomcn»  pcr«i^ 
inde  contingunt  m.vucm  ^oyleam ,  aique  tnzvt  liberO' 
orania  fervademe  ,  aiit  in  bypotl>cfi  Carttfianorum  co««* 
frimeute.  Egregic  adhuc  refclluntur  Cartcfiani  ex  Lc-^ 
gibus  Hydroftaticae,  quibus  docemur  fluida  amnia  prc- 
mere  in  rationc  compofira  bafi§,  &  altitudinis  \  ^V^^ 
^ttida  ejasdcm  fiint  ahicudinis,  pro  racioiRe  (bJius  bafis  j 

'  ^  proiix- 


ttsc  virhm.  ft  J 

jsroindc  explorata  altitudlne  ,  &  bali  (leris  inctimb«itift 

tacilc  detcrminabitur    pondiis  ,  &  prefllo  atmo(])h7rse 

tcrreftris.in  qiijECnnquc  corpora.     Atqui  vero  maieribus 

&pc  viribus,  aut  ponderibus  opus  e(l  ad  divcHenda  cor« 

pora  mutno  actra^a ,  quam  tit  pondus  «tmofphsrs?  (ic 

in  recitaro  Mnfchcnbrakii  experimento  cylindri  marmo- 

rei  cohsrrcbanc  vi  1 150.  librarum  \  cuo)  tamen  comper* 

tum  iit  pondus  columnx  atmofphzrics  in  bafim  duorum 

pollicum  Rhenanorpm ,    &  feptem    lincarum  prcmens 

non  prorfus  cxaeqnare  90.  libras  ParJfinas.     Sicpertica 

ferrea,  aut  lignea  bafim  habens  c.  c.  trium  digitorum^ 

incredibiiia  pondera  (ibi  appenfa  fuftinebh  ^  quin  mini- 

mts  cius  molecula?  diflbcicntur  ;   cum  interea  predio  at* 

mofphsrx  in  baiim  trium  poHicum  i^on  adscjiiet  ifli. 

libras,  ut  conficicur  inita  fequcnti  propprtione  :   (icut 

bafis  cylindri  (etrcuius)  cujus  diaipeter  ss    2.  poH.  7. 

lin.  ad  90.  libr, ,  fic  bafis  circuiaris ,  cinas  diatii.  =:    j. 

poli  ad  X.     Pollicibus  ad  19.  Hneasredudis,  inventa  po. 

ripheria,  ac  demum  area  bafium  circularium  ,  fa6la  depi« 

<jue  operatione  omni  invenietur  x  s    fere  ifti.  iineis. 

Ad  h«c  fi  preffio  aeris  caufa  fit ,  cur  vel  cylindri  duo, 

vel  molecuise  minimae  fltc  fibi   cohcreant  ;    oportebit 

lane  &  cylindros  e  diverfis  materits  confiatos ,  &  cor*. 

^forurn    omnirnn  niolecuias   minimas  eodem  modo  fibi 

cohacrere  (  ffqualis^nim  colunina  aerea  imminebit  fin* 

gulis )  ;    quod  faifum   cfic   teftantgr  cxpcrirnenta  ,  & 

obfervationes  quotidianaf.       Circumfpice ,   oro  ,    cor- 

pora  qujEvis  fortc  oblata  :  flt  alia  aiiis  denfiora ,  ac  fir- 

miora  efTc  deprehencles»     Accipe  cylindros  m$moreo$ 

fcho  illitos  ,  de   quibus   /upra  ?   cohserebunt  vi  1150« 

librarum  ;    cape  eburneos   ejusdein  diametri  :   nifi  vi 

200.    Hbrarum    non    coh^rebnnt.  Dices  :   Si  a^ 

iion  fit  caufi,  cur  fluida  figuram  (phvricain  aflumaiK,- 

nunquam  congrua  alia  ratio  phxnomcni  ifi:ius  rcddi  po^ 

terit.      ^.  N.  A.  rautua  fingnlarum  fluidi  partiura  ^t-» 

traf^io  in  caufa  efl.     Res  ficexplicatur  :  Fluida  cam  fj, 

guram  iriduercr  debent,  in  qua  eorundeoi  moiecul^  mi  m^ 

B  5:  niaB 


; 


ma^int  in  sqtiilibrio.  Jam  fi  Auida  in  txigua  qtiaDtiti» 
te  capiunrur,  (blum  in  tigura  {phn^rica  quslibet  vicin^ 
homogenes  particuli?  funt  in  squilibrio  ;  quia  tunc  fb» 
lum  eruiir  ejasdem  alticudinis  ;  ergo.  Certe  quscutw 
que  alia  figura  afTumatur  >  e.  c.  triangulariS)  vel  cubica^ 
(cmper  piures  particul^  fortius  trahentur  verfus  ccntra* 
lem  aliquam  molecuiam  ^  quam  vicinx  pauciores  ^  cudi 
attra£lio  omnis  babeatur  in  fatioht  direda  malTarum  / 
proiiide  coiumns  qusvis  viciils  tum  folum  xquiiibra* 
bunt,  cum  cruhc  ejusdem  altitudinis ;  quod  fir  in  figuri 
fphsrica. 

IL  Si  non  ab  aefC^  at  (altefh  «^  atbtre  ttmfriment^ 
re^eti  ponTunt  di£ld  pharnomena  ;  non  ergo  bpus  viribus 
attra6livis»  P.  A.  Licet  in  antlia  vacuo  non  habeacur 
aer  nativt  fiia  dchfitate  gaudens^  at  habetur  aer  maltunl 
expanfus  ,  aer  fubtiliflimuS)  quem  etherem  dicunc  ; 
crgo.  Qt«  N.  A.  ad  Pr.  D.  A^  habetur  in  vacuo  xther| 
qui  tamen  ob  fubtilitateih^  ac  raritateih  Hiam  omnia  cor- 
pota  permeat,  ac  proinde  tantum  internus  ilie  sther  re« 
fiitit,  quantum  exteriius  premkC.A.  hon  reiiilit  eodem 
modo  N.  A«  &Cm.  Si  aer  Intril  corpus  quodpiam  la« 
tens  communiCec  eum  aere  cxterno  ^  nuiluiTi  corpus 
comprimi  videinus ,  aut  figuram  immutare.  idem  ien» 
tiendum  -de  artherc  interno,  qni  cum  exteriore  illo  com* 
muniGat  Tum  vero  :  nunquid  iion  aerese  ipfie,VcI  «the* 
res  moleculae  (ibi  coha^rent  f  quX)  oro,  cohsfionis  iAius 
caufi,  (inon  attra£lio  ?  an  novns  iteruth  aerj  vei  st)ieif 
cas  comprimct  ?  fcd  de  ip(b  boc  qusretur  iterum  i  & 
qusretur  in  infinitumk 

IIL  Saltem  dicla  cohsfio  cylindrrrum  repeti  po« 
ted  a  figura  partium  >  &  di^fpofitione  ccrca ;  oportct 
cnim  eas  admodum  eflrc  Isvigatas ,  (ecus  non  cohzrc* 
bunt ;  uti  non  cobsrent  corpota  fuperficiei  afperas  ha* 
bentia«  sdo.  Sic  &  alia  pharnomena  txplicari  poflunt 
per  particulas  quaspiam  furcatas,  hamatas,  uncinatas  &c« 
^tio.  Numquid  juncus  unco,  annulus  annulo  cohsrct  pct 
figuram  J  proindt  &  roolfCttl«  minimat*      ]^.  N.  A# 

Cau* 


Lfxvirium.  "  ft7 

Caufalem  annexam  D.  oportec  eas  omnino  glabras  §fic^ 
qu«  fuperficierum  glabricies  cft  mere  occafionalis  canfa 
cohir(ionis  C  Caufalem;  qu«  iic  ca«yi  efficiefis^  nut  foT' 
vialis  N.  Caufal.  Sic  ftatuendum  i  polita  glabritie  fu. 
perficierum  pliires  moieculs  fe  (e  continguncai^ye///^i^i; 
cx  flhrium  partium  contatlu  phyfico  oric^r  major  cor- 
forum  accra£lio  ;  ex  fortiori  attradione  major  cohxiio ; 
acque  ita  glabrities  Cuperficierum,  conferens  ad />/(/rm/i 
molecuiarum  contatlus  fbyficos  occafio  audit ,  ac  veluti 
^OHditiOf  ut  corpora  {e  fe  fortius  attrahant ;  attradio  au- 
tem  CohjKlionis  caufa  formalis  dici  debct.  Nam  fi  l«vi- 
gatio  (it  cau(a  formaiis,  corpora  stqualiter  Isvigata  co^ 
hsrebunt  squalicer  :  policiora  etiam  fortius.  Fallit 
con^equ^ns  ;  igitur  &  antecedens.  Pr.  m.  Cylindri 
ehurnei^  quatumvis  a;flue  politi,  aut^politiorcs  marmoreis^ 
non  sque  c^hsrent ;  crgo^  Si  oggeras  :  fine  la^vigaris 
iiiperiiciebus  non  habeciir  cohatfio ;  ergo  l^vigatio  eft 
cau(a  cohxfionis.  :i^.  O.  A.  (ine  Isvigatis  Aiperficiebus 
tanquam  caufi  occafiouali  G.  A.  formali  N.  A.  &  C. 
Applica  vetu^  jllBd ;  Rncapproximatioue  non  urit  ignis ; 
&  tamen  approximatio  Cquam  vocant)eft  cau(fl  mere  occa» 
fionhlis ,  iive  conditio*  Idem  fit  dc  Isvigatione.  sdo. 
Moleculs  hamata  ,  fiircata^  uncinata  &Cf  figmentum 
ilmt  plane  ineptum  ad  explicandam  coha?nonem«  Quff« 
ro  enim  i  quid  tandem  eft,  per  quod  hami  &  unci  cohs* 
reant  ?  quo  abeunt  hami  ilii,  fi  metaila  liquantur,  aut  yU 
trum  in  pulveres  conteritur  ?  quis  hamos  reftituit,  dum 
liquata  metalla ,  aut  iiuida  alia  per  frigus  cojnfblidanturi 
3tio.*Annulos,  6c  uncos  fibi  mutuo  implexos  cohsrere 
p.er  figuram  lubens  admitto ;  neque  enim  omnem  co- 
hxfionem,  etiam  illam,  qwx  vulgaris  dicitur,  provenire 
ajo  ab  attra^iont ;  0cut  neque  omnem  motum.  Quis 
neiciat  multa  corpora  moveri  per  impulfionem  ? 

IV.  Si  cauia,  cur  di£li  cylindri  cohxreant ,  fit  at« 
tra£tio  :  omnia  corpora  fibi  cohsrebunt ;  omnia  enifn 
ie  £e  mutuo  attrahunt ;  iftud  vero  non  cxpcrimur ;  er- 
go«     ^.  D.A^  9mnia  fibi  cofastebunt  I  niii  eorundem 


ftt«rft£Vto  «b  Bttra6(ionibus  aliorum  corporum  Vinctmr  ^ 
aur  quoquo  modo  impcdiarur  C:  A.  ^cus  N.  A.  &  C. 
Quod  fepc  corpus  afperum  ^on  adharrear  pendulo  altcri 
itidcm  afpero,  quamvis  muruo  (c  rrahant,  &  trahantur» 
rario  e(l :  quia  corporum  iitorum  attra^io  vincitur  ^ 
trrraflwHic  tcrr*.  S«pe  vero  inutua  accedio,  aut  coh«. 
fio  aiiundc  impeditur,  ut  ab  inerria,  friclionc,  clafticita« 
te,  impuKionc  oppofira,  .medlo  rcGdentc,  &c.  Dc  cau- 
ialt  iftud  inrerta  noro  ;  omnia  fife  mutuo  attrabuut  in 
quibusdam  diflantiis  C.  in  omnihts  N.  in  aiiis  &  attni- 
hunr,  in  aiiis  repdlunt. 

V.  Vis  attradtiva  cft  qnalitas  Pcripatctica,  jnrc  opti- 
ino  c  Schoiiscliminanday  crgo.  Pr.  A.  Qualiras  oc* 
culta  diciuir,  cujus  cau(a  i«noratur,  licct  ph;cnomenon 
fit  manifcftum  ;  at^ui  \  crgo.  ^.  N.  A.  Ad  Pr.  D. 
A.  qualiras  occulra  eil,  cujus  caufa  ignorarur,  &(imul: 
mjm  ex^kntia  ex  obfervutis  effediBus,  aut  exferimentiA 
evinci  neqnit ;  per  quam  nibtl  explicatnr ;  quee  affumitnr 
*ad  pbauomenon  quodpiam  explicandum  ,  quin  o/tendatt$r 
reliqnas  propf  ietates ,  quas  corporibits  tneffe  conflat ,  ayt 
caujks  mechanice  agentes,  explicando  pbanomeno  ueutiquaot 
Ji^cer-e ;  cujus  ieges  ignoraftmr ;  qua  ex  praclara  iUa 
tnauria  Peripatetica  edticitur  (  nc(ci«,  an  no»  crccrur  )  ; 
tujjts  erigo  plerumque  a  diverps  corporum  fpeeitbns  repeti 
folet ;  qua  ita  corporibiis  itHrinfeca  fingitur  y  ut  ^  wfi  fu^ 
fernaturaliter ,  ab  iis  feparari  non  pojjit ;  qua  exigit  /W- 
h^rere  alteri  tauquam  fini  cui  adaquare  a  fe  diflin&o , 
C.  A.  ctijus  duntaxat  cau(a  ignoratur  N.  A«  &  Cm. 
Tanta  idhsc  criminatio  longani  fibi  depofircbat  rcfpoii- 
fioncm  ;  dedi,  eamquc  iatis ,  poto,  claram  dedi-  Jaoi 
vidcndnm ,  (i  bornm  aliqui^  convcniat  vi  attrafiivx. 
I.  cjusdcm  cxiftentia  invi^is  argumentis  ioco  (iiperiore 
eft  comprobata*  II.  pcr  cam  tantutn  non  omnia.  ph^- 
Aomena  esplicantnr,  nt  patcbit  in  decurru  tra£lationis 
liajas  phyficr ;  adeo  falHim  cft  jiibil  per  eam  cxplica- 
ri.  III.  Oftcndunt  Neatoniani  caufim  quamconque  ex- 
ternMD  ftcundiiai  \icQsa  mecbanicas  agcntm  explicandji 

attra* 


Lex  virium.  ^9 

ittraSioniifn  pbsnomcnis  iniiume  idoneam  efle ;  ^d 
requiri  vitn  arrahentem  etiam  a  cftteriscorporutii  proprie^ 
mibus  muitum  diverfam.  IV.  Attraftionum  leges  non 
ignorancur,  quas  loeo  fuo  fnbinde  recirabimus*  V.  Non 
tll  artraclio  entiras  aiiqna  ahrolota,^qits  ex  m.iterii  eda- 
eatur.  Educiionem  forma-  ciijujcunqucexeciaiifur  ho* 
dicrni  Phflofbphi.  •  Vi«  Non  clt  quaiiras  fpecrfica  h«. 
jns  dercrminati  corports  C  qualem  efTe  dicunt  Pcripate* 
tfci  Anripcridaiim ,  Sympathiam ,  Anripathiam,  &c.  )  ; 
(ed  aniverfolis  eft,  ac  primitiva  corporufti  propnetas, 
conveniens  omnibus  mundi  corporibns ,  fic  fitogulis  ma« 
teriar  partibus.     Omitto  reliqucw  duo  \  nagie  (nnt. 

VL  Per  attradionem  nihil  explicarur  ;  ergo  cft 
qualitas  Vcripaterica.  P*  A.  cum  per  attraf^ioneni  ex- 
plicantnr  phxnomeni  ,  expiicatur  idem  per  idem  ;  it« 
qui  fi  iftud  :  nihil  per  eam  explicatur ;  crgo.  Pr.  M. 
per  atrridionem  explicarur  a£lio,  per  quam  corpora 
mutuo  acccdanr ;  arqui  arrraftio  nibil  aliud  eA  ,  quam 
ipfa  h£c  a^io,  per  quam  corpora  ad  (e  (e  accedunt ; 
crgo  explicarur  idem  per  idem;  ^.  N.  A.  Ad  Frob. 
N.  M.  ad  hujus  Pr.  D.  M.  per  atrraflionem  fiimprani 
cam  parricnlaribus  legibus ,  vel  cum  applica^one  legis 
generalis  ad  particulares  circumftanrias  explicanir  mu* 
tua  corpprum  accefiio  C.  M.  per  nudam  arrradionem 
N.  M.  D.  criam  m.  attra£^io  eft  ipfa  hsc  a£li^,  pet  > 
quam  corpora  accedunt ,  quit  rnmen  dam  explicatur , 
probitnr  efTc  conformis  legibos  C.  m.  quin  talis  efie 
pFribetur  N.  m.  &  C.  dicendum  porins  :  per  lcges  at- 
trac^ionis  expiicari  mntaam  quorundam  corporum  aC- 
tcflionem,  quam  per  attradioncm  ip(am.  Quid?  quod 
dici  eriam  poreft :  per  $ttra6)ionem,  (ea  a&iohem  e.  c. 
corporis  B  explicari  accefllim,  (ca  a£lionem  corporis  A  - 
(^.  8.  Scboh  IJ.  )  ;  arqui  a£lio  corporis  A  non  cft  ca- 
dem  cam  aftionc  corporis  B  ;  crgo  dam  per  atrra£^io* 
nein  expHcatar  corporam  acceffio^  non  explicatar  idcm 
per  idem* 

VII. 


A 


30  SfSthL  CaputlL 

^  Vn.  Attradlio  nullis  arguinentis  detnonftrari  pO^ 
teft;  ergo  adhuc  dici  debet  qualitas  occulta.  Pr«  A. 
S\  pofibt  i  tum  cx  ph^nomenis ;  cx  iftis  deroonftrari 
non  poteft ,  probarctur  enim  idem  per  ridcm  ;  erg«. 
Pr,  m»  attra^io  prObarctur  per  phxnomena ,  &  ifta  vi- 
ciilim  per  attraftionem  ;  ergo.  15^.  N,  A,  ad  Pr.  C. 
M.  N.  m.  ad  «It.  Pr.  D.  A.  attraftio  probaretur  pcr 
pharnomcna,  &  ifta  viciflim  per  attratlioncm^  divcrfo  xa- 
mcn  gcncre  dcmonftrationis  C.  A.  codem  gencrc  Aj^"" 
monftrationis  N»  A.  &  Cm.  dum  ex  phsnomenli  Ai^ 
monftratur  attraftio ,  dcmonftratur  a  pofteriori  ;  funt 
enim  phacnotjicna  ^tf^i/j  attra^ionts  \  dum  ex  attra^ljor 
ne  dcn^onftrancur  ph^nomcna,  dcmonftrantur  aprio/il 
cft  enim  attraflio  cauja  pbanomewrum.  Divtrfa  hkC 
demonftrationum  f}:>eciei  cum  adhibetur,  idcm  nonpro« 
Katur  per  idem  eodem  modo  fumptum ;  <juid  ni  vero  liceac 
probare  idem  per  idem  diverfo  modo  acceptum  ?  Licct 
fane  Carteiianis  ita  argucre  :  corpora  funt  impenetrahi" 
lia  i  igitnr  fe  fe  excludunt  a  loco  ;  &  viciftim  :  corpora 
fe  fe  exclhdunt  a  loco  ;  funt  igitur  impenetrabiliat  Licct 
Philofophis  omnibus  fic  ratiocinari  :  Sollucet;  ergo  dies 
efi ;  &  iterum  ;  dies  efl  ;  ergo  Sol  lucet ;  quin  tamcii 
aut  Cartefianus,  aufcujuscunquc  feftae  Philofophus  alius 
jn  lcges  argumentationis  £e  dciiquinb,  aut  idem  pcr  idcm 
probavifte  exiftimet.  Licebit  etiam  nobis*  ,  Denique 
attra£lio  quidem  per  phaenomena  probatur,  &  h^c  pei: 
illani;  (ic  tamen :  ut  per  attra£lioncm  ^x  a//Vif  quibus«' 
jdam  phanomenis  cognitaln  cxpUccntur,  &  probentur 
Mlia  deincq>s  phanomena. 

VIIL  Clara  attradHonis  idca  haberi  nequit;  ergo 
pcr  flttraftioncm  nihil  explicari  potcft,  explicaretur  enim 
oibfcurnm  per  obfcurum.  Sed  qu^litas,  ner  q\iam  nihil 
explicari  potcft,  cflr  qualitas  Peripaterica  ;  crgo.  'BjL* 
N.  A.  quidclarius,  quam  cum  attra4lioncm  dicimus  cC 
£e  determinatibncm  ad  acceftum  mutuum  ^  Ontologot 
latcre  non  debct ,  quid  indifferens  fit ,  quid  determim' 
tum^      Vulg(us  addo  bominum  iatere  non  potcft ,  quld 

acacG 


Lexvirium.  31 

acceflio  fonet,  quid  rcccifio.  Scd  iteriim  ad  intpettetra^ 
iilitatem  provocetnQS  adver(um  Carcefianos  talibus  ple- 
rumque  argumcntis  depugnaiites.  Ifti  clarain  impeuetra* 
iilitatis  ideam  (e  cxponere  putant ,  cum  dicunt  :  c^Te 
•proprietatem  ,  vel  afFe^ionem  corporum  univerftkmy 
vi  cujus  quodcjue  carpus  ex  eodcm  loco,  in  qao  ipfum' 
cxnHt  y  excludit  aiia  corpora  ,*  quibus  quidem  voeibus 
snagnopere  (atisfaciunt  omnibus ;  qpare  &  ipfi  ,  fi  paria 
in^^r^m  noftraih  damus  verba  ^  fibi  (atis£i£tum  exifti« 
ment; 

IX.  Num  vis  attrahens  pendeat  a  libera  DEI  lege  : 
an  ex  ip{a  materis  natura  profluat ;  fitne  repetenda  ab 
aliquo  tertio,  definiri  non  poteft.  Sic  etiam  ,  fitne  fub* 
ftantia ,  an  accidens ,  dccilum  hucufqu^  non  eft  *  ergo 
non  hahetur  clara,  &  diftinQa  attraC^ionis  i^ea*  ]je. 
C.  A.  P.  C.  ergo  non  habetur  diftindaj  &  adaquata  at« 
tra£tionis  idea  C.  C.  inadaequata  Ni  C.  Quid  h$e  fibi 
Yoces  velint,  docet  Logica.  Csternm  fi  dicai  vim  at- 
trahentem  proficifci  a  iibera  DEI  legc,  &  voluntate, 
quid  eft,  qu.bd  opponant  adverfarii  ?  an  non  ipfimet  iftt 
afHrmare  idem  coguntur  de  impenetraiilitate  ^  vi  centrh 
peta^  centrifngay  &c.  ?  Clamant  :  indignum  efle  Phi- 
lofbpho  in  explanandis  naturs  phsnomenis  confugere 
ad  DEUM ;  fic  nempe  paucis  Phyficam  ab(blutum  iri  ^ 
fi  pro  fingulorum  efFe£);num  caufis  reponatur  %  quia  Deut 
voltiit.  Sed  pace  iftorum  reddam  ego  x  nunquam ,  qui 
Neutonum  fequuntur  ,  pro  effeSuttm  caufis  affignant 
DEI  voluntatem,  (ed  vircs  ;  dc  quibuii  tamen  ipfis ,  & 
de  quarum  legibus  hodie  qusritur,  fintne  re  vera  iikx^ 
&  non  alise  a  DEO  conftitut^.  Nec  ioc  erit  paucis  Fhy/u 
€am  abfolvere  pro  fingtdorum  effk^utmi  caufis  reponendo  s  ' 
^tia  DEVS  voluit  j  ut  mcpro  caufis  ipfit  iti  aliorum  fen»- 
tetitia  repotpi  dehet  r  Qttia  rerum  natura  exigit,  Ipfa  iUa 
Cotiditorif  volutitas  inquireuda  e/i,  i^  iUa  ipfa  qtianquam 
libera  hges,  qnibus  hac  erdinatiffima  tmverfi  compages  tam 
apte  isner  fe  cobaret,  fiJ'  dottec  ipfi  libuerit^cobctrebit.  Verba 
iimt  BosaavicUi.    Qagd  4efub£kptia,  &  accidcnte  ad. 

ditur. 


3a  ScmoL  Cs^uill. 

ditar,  ftd  eos  remitto,  quibu»dcfinire  anitnus  eft:  fitne 
?is  attraaivi  corporibas  iHtrinJeca^  an  extriufica ;  it«n : 
an  omnc,  quod  in  natura  cxiftir,  fnbftantia  fit,  vcl  acci' 
deiis.  Qiiid  autem  li  tcrrium,vcl  quartum  aliquod  ha£le« 
nus  m«nti  noftrje  incognitum  exiftat  praeter  fubftan- 
tiam,  &  accidens?  Ego  interea  ex  advcrfariis  qusram 
ailiduo  .*  quid  illis  dicatur  impeuetrabilitas  f^  ^  Quid- 
quid  ftatilant,  novcrint  idem  eodem  jure  de  vi  attra- 
bente  conftif  ui  pofTc. 

X.  Vis  attrahcns  cft  principium  tribuens  corppri- 
bus  a£(ionein,  quam  Neutoniani  adeo  tpG  (atis  iibi  ex- 
ploratim  ison  cfte  ultro  fatcntur  ;  ergo  fairem  afBnis 
cft  qualitati  Peripateticse.  ^.  O.  A.  fatcntur  cam  fibi 
iion*(atis  cxplorfitam  cflTe  quoad  omnia  adjun^la  C<  At 
quoad  eflentiam ,  aut  ad;un£lorum  aliqua  N*  A.  &  C« 
Leges  attra£lioni$  tam  fvint  explorat»,  ut  eciam  demon« 
ftrats  habcantur» 

XL  Qu$  dantur  vircs ,  &c  proprietatcs  corporum, 
in  vi  inertis  fundari  ^debcnt  ;  fed  vis  attradiva  in  ifta 
non  fundatur  ;  ergo  non  datur.  Ita  Eulerus.  ^. 
D.  M.  vires,  &  proprtetates  derivata  fundari^dcbent  in 
vi  inertijB  Q.  M.  primitiv<t  N.  M.  C.  m.  &  N.  Cm. 
Vim  attralicntcm  voco  materi^  proprietateni  generalem; 
&  primitivam.  Quanquam  quid  ifta  virium  difcretiene 
opus  eft  ?  Dicam  breviter,  &  plus  dicam,  quam  objcdio 
pofcit :  ph;rnomena  attratlionis  ncque  per  folam  yim  in- 
cxti^y  ncque  per  aliam  aliquatn  bucnfnjiie  nctam  corporis 
prcpriesatem  explicari  polfunt  Dcbet  ergo  admitti^ 
vis  diftin'6^a,  quam  quocunque  nomine  compcllemus, 
oihil  intereftt     Nobis  interim  attradiva  dicitur.' 

XII*  Licet  piurima  phfnomena  explicari  ncqueant 
per  vim^inertie,  non  tamcn  re£le  arguitur  ipfa^  non 
pendere  a  vi  inertiie  ;  ergo.  Pr.  A.  Licewin  plurimis 
corporibus  non  obfervetur  vis  iuertiS)  nemo  tamen  re- 
3e  intuleric  non  dari  in  corporibus  omnibus  vim  iner- 
tix ;  ergo  a  pari.  ^.  N.  A  fim^l  notatum  yolo  : 
non  modo  plurima  fJfitMmeua  pcr  (olam  vim  inerti^ 

cxpli- 


Lix  virium  3} 

•xpHctri  mn  pofle,  (ed  ^mtM  uuBay  cft  enim  vis  iner* 
tjx  oppofi»  attrabenti  >  icilicet :  per  vim  inertis  jihi^ 
nnr  torpos  eonie^are  flattim  Gium  ^  per  attrahentem 
teminiio  mutai:i  tlebet  ftatas  eorporis  attradi »'  agit  c* 
KMm  attradio  in  ratione  reciproca  daplieata  diftantia- 
ruoK  Inde  facilts  re^onfio  eruitur  ad  Pr: .  lii  omni- 
fcui  umverA  corporibus  admittinius  vim  inertis ,  quia 
jm  tu  omaibus>  qvLX  ob(ervanius,  advertiinas  dari  vim 
tnertin  ;  argamcntiim  itaque  defiimi  potefl  ab  analogta 
corporam  aKbrum*  At  in  nallo  corpore  ob&rvamui 
phonHrmcna  qtisepiam  attradionls,  ut  motum  accelera» 
Tum,  vel  reftrdatum  proficilci  a  (bla  vi  inertis ;  dicen» 
dum  «rgo  :  nulla  phsnonien«>  qu£  ab  attradione  in 
i^fteniate  Ncutdniaaoram  repeti  Coltnt^  per  vim  inertic 
«xpiicari  pofliu 

XIU.  Visinerti^adver&tarvt  attrafiivz^proinde  il* 
tcrutra  non  datur ;  datur  autem  vis  ioertic  ^  non  erga 
tdatur  vis  «ttrafiiva.  PnM»  R  datur  utraque,  babebic 
idem  corpus  nifus  oppefitos ;  atqui  babere  non  poteft; 
tevgo»  Pr.  M.  vi  inertix  nitetur  corpos  c%  c»  quie£:ens 
^iRcej^s'  qaicGrcrc  :  vi  attra£tionis  ftitetur  aceedere  «d 
corpus  attrahens>  qui  nifiis  fi  oppofiti  non,  funt,  netcio, 
iqiiid  oppoiitum  dici  debe«t«  j|2>  i  mo^  atqui  attra£kiv« 
Via  non  dicitur  inelTe  cOrpoci  per  «ttra£iionefli  dutrmi^ 
na$o  ad  celerioreni  motam  y  l^  dfHrmiuauu  (  §•  %s9 
ScheU  IL);  crgo.  ^»  ido  D.  M.fvis  inertic  adver(atut 
vi  attrahcnti,protndc  alterutrA^  nc^  daturpoftconflidam 
T%  M.  in  conili£hi  ftAd.  non  datur  fine  vilEloria  C>  M«. 
xum  viftoria  N.  M»  C.  m.  &  N.  Cm.  Datur  imo  poft 
mnflidam  vis  inertidB»  qusc  compom  poffit  cum  ctfe£tU 
ims  vis  atcrahcntis  ;  &d  da.tat  vu  in^rtia  viSu  ; .  hino 
dixi  T>  M>  Neque  filc  aliquid  «  Communi  Keutonia* 
tmuirv  CcnCvk  aiienum  dixi^  jaxta  quos  corpas  delabetsi 
tcmpu&ato  lecundo  con(erv«t  pef*  vim  imrrid  celeritii* 
lem  ptioti  tempulcaio  faabit^tni  &  per  vim  acceleioici» 
tom  ijQs  iacmiiciuttfli  acqairith    Sfd  dc  lioo  «libk 


34  S^ot  CapuilL 

^       XIV.  Ircratn  Buhrum'!oh)\cicnvct!;i  rcatzt  ScberffcJ^ 
n/!fVVires  fe  babent  ut  colores ;'  (ed  nequeunr  m  eo^ 
dem  corpore  efle  piores  colores,  qaoram  unus  in  aitero 
sion  contineatur ;  ergo  neque  plures  vires,  quarum  ana  ^ 
non  contineatur ,  aut  certc  fundetur  in  altera.     Sed  vis 
aitra£^iva  nec  continctur,  neque  fundatur  in  iaitera ;  ergo  ' 
fi  datuf  vis  inertix,  non  datur  vis  attra£Hva.     J^,  D.  M. 
Vircs  sotales,  £eo  t«ta  virium  cdle£lio  ft  habct  ut  coloret 
C*  M.  vires  partiales  Subd.  habent  (e  at  coiores  refpc* 
&vk  eiFef^uum  partialium,  cmque  vi  inadxquatx  refpono ' 
dentium  C.  M.  refpedn  virium  totaiium  N.  M.  C.  m. 
&  D,  C.  ergo  neque  plures  vires  aiaquata  C  Cm.     //i. 
adaquata  N.  Cm.       EfEeftus  pleni  iimt  proportionalcs 
caufis  fuis  adaequatis  (  §.  f.  Schol.  I.  )  ;    crgo  pr«ter 
cau(am  adxquatam  alit  refpeSu  ejusdem  eflcttus  (uftine- ' 
rt  non  pote(t     In  cafu  e.  c.  motus  acCclerati  caufa  ads. 
qnata.eft  tam  vis  inertiie,  quam  attra£liva;  ergo  practcr 
has  quidem  duas  alia  admittenda  noneft^  fateor;  non 
autem  prster  (blam  vitn  incrtis. 

XV.  EfFc£lus ,  qui  atrra£lioni  tribui  (blent ,  ad* 
Ibribi  poffant  irapulfionibus  corporum  cxtrinftcorum  , 
quemadmodum  frequcntcs  alii  motus  iisdcm  tribuun- 
tftr:  Quid  ?  quod  Nemoiias  ipfe  Princip.  Mathcm.  L.  f. 
Scct.  XI.  ita  fcribit :  ^am  ptTgo  motum  exponere  corpo^ 
tum  fe  mutno  trabentium ,  eonjlderando  vires  centripetaf 
tauquam  attraSiones^  quamvis  fortap  ^  fi  pbyfice  loqua^ 
tnur^  verius  dicantur  imptilfm.  ^.  D.  A,  adferibi  ppC 
funt  impulfionibus  tn  majore  diftantia  agcntibus  in  ra- 
tionc  dirccra  maflarum ,  &  rcciproca  duplicata  dift^n» 
tiirum  C.  A.  juwa  alias  legcs  agentibus  N*  A.  &  Cm. 
Iihpulfioncm  Cc  flc  non  ^iia  Icge  agcntctn  dicimus  at- 
tractiohem.  Periadc  tamcn  fucrit,Icu  attractioncm  di- 
cas ,  fcu  impulfionem ,  mbdo  rcm  candem  intclliga§ 
fub'duo1nis  tiominibus  ;  ijcqac  cnim  dc  vocc  litigarc 

pVacct. 

XVI.   I^offta  a«ractionc  fcqtii  ncccflc  «ft  abford* 

mtiltfli   4.  Lapis  ponc  tuf hm  cadens  attraheretur  a  vxt* 

rii 


Ux  virium.  %% 

Ai   proindefQe  ftd  cerrtin  iiQfiqtteni  pertingeret.    1|^ 
Sphsc^  gemcna   phyiice  (e  eontingente»  eohmrtmit. 
lil.  Non  peffct  poodos  onms  Hbr«  ievari  a  eerra  coi 
sncumbit ;    ftteraheretur  enim  in  rarione  cUrefit  .maflb 
aittraben)it|  five  terrc,  &  reeiproca  duplicata  diflaatic  t 
b.  e*  prout  quadratum  diftanttflB  mtnueretnry  fic  cnC^ 
ret  attraftio  ;  pondus  vero  terrft  tncnmbent  nuUateiHit 
•  terra  attrahente  diftaret ,  fiiltefn  od  Ittifiim  ;  ergo  itt« 
finlte  attraheret,nr.     Sed  fi  iftud :  non  pofiet  lefori  aMr« 
pu%  ;  ergo.     IV.  Corpera  qerrit  ex  eadem  altitodino 
dciabentta  cqualiter  attrafaerentQr ;   ergo  cqoali  celeri* 
tate  caderent.      V«  Corpora  bmnia  in  fiiperficie  terrs^ 
aiot  (altem  in  lcftgatit  foperfickbot  locata  mutuo  aeoedero 
dcberent.     VI»  ExhaUtionct,  6c  vaporet  neutiqnam  tC 
forgerem*     VIL  Daretur  aftio  in  diftant ;  fic  magnce 
•gcret  in  ftrrom  fibi  minime  comiguum.      Mitto  {Mnri^ 
jRB  alia  abfurda,  qoc  ex  (yftemate  attraftioitis  manifefl» 
«onteqoontttr.     ff.  N.  A.  ad  Pr.  admitto  trabi  lapident 
o  turri;  (ed  oego  fere,  otnonqoam  pertingat  ad  terram; 
vincitor  enim  attradio  torrit  ab  ettradione  terrr,  com 
ttteradionet  fint  in  ratbne  direda  maflartHn  trafaentioiit* 
Tom  ex  con>onfl:a  illa  torris,  terntqoe  attra8ione  dnsi* 
taxat  (equitor  :  lapideni  omnino  perpendiculariter  non 
decldercyOtneqoe  caditlapit  emalo  navit  demifius  (qao4 
ob(ervatam  eft  ab  hominibot  in  littore  confiftentibnt ) 
eom  interea  aquaa  {iilcaret  navit.      A^  II.  Sphtrrs  ge* 
mins  non  coh«rent ;    cura  enim  {econdnn  paucat  fa# 
perficiei  palrtet  &  Ce  contingant ,  necefie  eft  mutoaio 
eorum  attra£lionem  prorfiit  exilem  efie»      Ad  III.  JMe# 
go  pondot  terrc  incumbent  non  diftare  a  terra  ;    fciii» 
eet  I  cum  de  attrt^ione  agitor ,  diftantia  corporit  tt» 
fra^i  repetenda  non  eft  a  foperficie  terrc  ,  fed  eb  qot» 
dem  terrje  centro.    Ad  materiam  di  gravitau  docelio^ 
%uemadmodum  omnet  (phsrc  partea  eodem  mpdo  at 
trahant,  ac  fi  in  cemro  eoiicdc  efifent;   (eo :  tanquam  fiT 
tis  tota  prodiret  de  corpolcoS^  unico  in  centro  fph«r« 
denftitoto«  -  Ad  IV»  «Corpttt  4ivirfie  \^  maffis^  Sn 

C  %  90h* 


y 


35  StShl.  OftaW 

mimhit  prcdita  m  vacuo  qaidaia  cqtiili  rdladrat^ 
deut^untur  cx*altiradine«qu«li }  at  non  f»  apriciy  ubt 
ratio  habenda  eft  tani  tnaffamm^  quam  volumittUfn^  quia 
iuperanda  eft  re/^hmia  aeru*  Arque  licet  corpora  di« 
TerArum  maflarum  cjusdem  fiot  voluminia^  ac  proinde 
«quaiis  coiumna  aerea  refpondeat  fingulii ,  non  tameia 
eqnali  celerirate  delcehdent,  quia  « tnaffa  majm  facilius 
Vincitur  reiiftentia  aeriSi  quam  a  miuare.     Ad  V.   Cor« 

Eora  omnia.  in  fuperficie  terrie,  aut  (altem  in  fiiperfieie- 
ns  laevigatii  pofita  miituo  accedere  deberent,  fi  eorundein 
motui  aliande  non  impediretur  C.  A.  cum  impediatuc 
N.  A.  &  C.      Impedimenta  motus  eflfc  pofiTunt  iuertia^ 
friStio^  mtdium^  atftaSio  aliorttm  corporum  Vc,     Hine 
ctiam  ratio  patet,  cnr  non  omnia,  qust  mntuo  Cc  &  tra» 
hnnt,  in  acervum  unum  coeant.     Ad  VI.  Exhabtioncs^ 
&  vapores  lion  afliirgercnt,  nifi  afiionc  ignium  fiibterra* 
neorum,aat  fermentationibaaunde  unde  ortis,vcl  deniqua 
aliis  quibnsvis  dc  caufis  excuterentur  cum  vidoria  at« 
tra£Honis  C.  A.  poftquam  ita  excutiuntur  N.  A«  &  Cm. 
Ad  VII.  Daretur  adio  in  diftan^^  (eu  ulis,  qasr  effe£luni 
«liquem  phyficum  producat  in  (ubjeCto ,  a  qno  rationo 
loci  disjungitur ;  quin  ad  effedum  hunc  corpus  aliquodl 
intermedium  coneurrat  T.  A.  nam  fi  vis  attradiva  coiu 
poribus  non  fit  intrin&ca,  nuila  dabitur  a£kio  in  diftans, 
«t  confideranti  patet.       Qux  fierct  in  (ubje£lum  extre 
^hsram  a£livttatis  pofitum  N.  A.  QtC,     Qoi.  aflionem 
in  diftaiis  priorc  fimfii  intelle&am  propugnant  ^  eos  ab 
omni  vel  (ufpicione  abfurdi  cujuspiam  admiili  prudent 
quisquc  Philo(bphus  ab(blvet ;   ficut  adver(arii  ipfi  ab* 
furdum  tlihil  (e  admittere  exiftimant,  cumajunt  t  qot^ 
pusflffcnSi  fivc  caufiim  non  ciTc  in  eodcm  loco^  in  quo 
cft  (libje^um,  quia  non  con^penerranrnr.    Dicuut  Pfrim 
fatetici  i  Licer  c4a(a  non  fir  codem  in  loco ,  in  quo  eft 
iubjef^ttm  I  at  adio  propagatur  pcr  (nbjedam  qaoddam. 
mediam  cau(am  inter,  &  cfFedum  ;  quo  pofito  toUitur 
aftio  in  diftans^  &  abfurdum  omnc.      ijL*   Ideo  iflu4 
4bceri  a  Pcrif ateunil;  fm  iScSqi  |r«4«ft«tl  conftituuol 


V 


.    Iax  viriumi  %y 

in  qnftlttaribot  qtiibiMdain  corpori  ihhmntibai »  qm^ 
wmraliter  nanquam  fine  (abjeAo  haberi  pofle  WxSS»^ 
mant ;  hinc  in  eorum  (ententie  qutittates  primum  cfR- 
ciuntar  in  (ubjedo  cau&  contiguo,  five  in  medio  ;  ab 
liis  iterum  iii  vicinis  corporibas  producuntar  ali^  ejos* 
dem  generis  qaaiitateS)  &  fic  deinceps ,  donec  ad  (ubje« 
Aum,  (eu  effedam  ip£um  deveoiatiir^  Faliuntur  vehe» 
menter  :  non  enim  adio  efl  qualitas  requirens  (iibie* 
Aam  medium  cauiam  inter,  &  efFedum*  Dicum  Car* 
tefikui :  Eodem  in  loco  non  cft  caufii  agens  ,  in  quo  eil 
fiibjedum  j  (emper  tamen  caufa  fiibiedo  eft  cwtigua; 
quo  conftituto  iternm  omnem  a&ienem  in  diftans  tolU 
viecefile  eft.  i^,  Illud  Cartefianorum  de  contiguitate 
dogma  natom  eft  ex  eo  ,  quod  nullam  tdionem  eflb 
putcnt,  nifi  qus  fiat  per  impalfioncm  ex  coliifione  cor* 
porum-provenientem.  Faflontur  &  ifti  non  modicc; 
•ut  certe  impulfionum  leges  ab  iis  conftitutas  faliere  ^ 
cportct,  cum  illis  phxnomena  impuKiuim  non  refpon- 
deant.  Sed  dabo  interea  liberaliter  s  corporum  contiguim 
tatem  requM  ad  aSimem.  Qucram  tamen  *  fitne  con- 
tignitas  prificipium  aliquod  a&ivum  ^  Non,  iiiquiunt» 
.itd  mera  eft  cotditio  ad  agendum  reqaifita.  Bcne  ha» 
fcet.  Ergo  fi  contiguitas  :  cur  non  alia  quaevis  di(bn«* 
fta  eiTe  po(l|it  conditio  ad*agendum  ?  Sane.contigtiitat 
non  magis  eft  relativm  duorum  corporum  coexificndi  ma* 
Jus,  ac  quxvis  alia  diftantia.  Liberent  utrique  (  C^te* 
fianos  intelligo,  &  Peripateticat )  animufn  ab  errorib)is 
quisque  (uis,  &  a£Konem  in  diftans  (altem  in  rerum  M* 
tura  foftineri  pofte  nobiscum  affirmabiint« 

ScifoL  IV^  Contra  vires  repulfivas  obiiciontur  (& 
qtientia  t  I.  Dator  in  materiai  five  in  corporibus  vis  at* 
tradiva  (  $•  15«  &  14- )  >  ^go  "Oi^  d^tttr  vis  repulfiva* 
Pr.  C.  vires  attra£tiv«,  &  repailivsc  fiint  vires  oppofitc  ; 
led  ineodcm  iubjedo  neqoeunt  efle  VSres  oppofitc  \  er« 
go  6  datur  in  mtteria  vis  attraSiva ,  non  datur  vis  ror 
puifiva^  Pr.  M.  Vta  «ttradiva,  &  repulfivt  tendunt  ia 
4^Pf  oficnm  i  crgjO  fiEint  vires  oppofitc*    P*  A.  Vis  attr^»^ 

C  J  Sivt 


J 


31  St9kt  afuiJL 

«^[hra  dte«f|nifiit  td  mntaam  tcceffionem  »  rcpnlfift  tA 
ffimlam  fugam  j  fed  (ic  tendunt  in  oppoiitum  ;  ergo* 
mt  C  A:  N\  C.  Ad  Pr.  N.  M.  ad  ulc  Pr.  D.  A.  Vlt 
•ttra£liray  &  repulfiva  tendunt  in  oppoiitum  re(pe£lti 
o^e^H  diirerib  modo  conftitati  C.  A.  eodem  modo  fnifl* 
pti  K.  A.  6cCm*  dum  eorput  idem  jam  attrahitor,  |aat 
f«pellitary  m  aiU  (emptr  di/iautia  tttrahitur^  in  alia  rt« 
petiitur.  Nafcittr  ind^  objedorum  diverfitas ,  qnx  om« 
)nem  tollit  oppofitionem ,  non  (eeat  tt^ao  repugntntin 
dmnif  toiiitttr  tn  Ible ,  qui  non  modo  ?im  babet  ixfic* 
§m§di,  Ud  &  flotdt  Peddendi  ^iffSa  siiverfa,  fire  «/it , 
&  t/it  «w4a  diJf^kM. 

IL  Alit  (k  tlit  difitntit  non  toHit  oppofitionem  ; 
tdbae  ergo  vis  tttrtSivt,  &  repulfivt  fibi  opponentur. 
^.  A.  Difttntit  nihil  eft  retie ;  ergo»  "Bj^  D.  A.  Nihil 
«ft  retle  Mhfolmtm  C.  A.  rtjftSivum  K.  A.  &  C.  Dt- 
lUntit  eft  reittio  quardtm  Dinoram  modornm ,  qoibm 
fcint  corport  vel  pundt  extftant«  Quod  doo  corport 
mtgts  t  ie  diftent,  vel  mtnus,  eft  aUquid  m>n  mere  imt* 
^iiuriami  ied  naiittt  diverfom, 

Ilf .  Si  dtretnr  ▼ii  repttlfivt  ia  qoiboedam  difttnttit, 
minimis ,  debtret  ctrtt  qocpitm  difttntit  Phyfi. 
•e  dettrmintre  vim  repaifivtm ;  ttqui  ifltid  dici  nequit  \ 
MO.  Pr.  mf  Determinttio  Phyfict  eft  aAio  ;  ergo  fi 
difttntit  determintret  Phyfice  vim  repuifivtm,  tgeret  ia 
«tm.  Non  totem  tgit ;  ergo.  ||e«  €•  M*  N.  m.  A4 
Probttionem  D.  A.  Determtnttio  Phyiict  profeAt  a  tam* 
fa  effiQiifne  eft  t£kio  C  A.  a  primifio  fiopiam  txiraim 
|l.  A.  6cC«i.  Principiom  dicituri  «  qoo  objednm 
sfooainqoe  modo  ptndet ;  vel  i  qoidqasd  eft  rttio  folfi* 
«tens,  ex  aoa  intelligi  poteft^,  cor  res  tliqot  potios  fit, 

Jotm  non  nt ;  ttqoi  t  otfttntit  pendet  ▼!•  repolfivt ,  dC 
ifttntit  eft  ttiis  ratio,  n  qat  intelligi  poteft»  cor  ris  re* 
f  oifivt  potiot  htbettor ,  qatm  vis  tttnftivt ;  ergo  d^ 
lUnttt  iOi  prind|ian  ?is  fepolfivti* 

iVi 


\ 

V 


Lix  viriunu  39 

IV.  Diftintia  non  poteft  eflc  principiam  vis  rcpnl' 
fiv9  *,  ergo  diftantia  non  poteft  PhyGce  deteriniha^iig^ 
repnlfivam.  P.A.  Diftantia non poteft  inodificarcvim, 
&  proprietatem  corporis  ;  crgo  nequic  eflc  principium 
Vis  repulfivap.  Pr.  A.  I.  Diftantia  cft  nihil ;  crgo*  II. 
piftantia  nequit  imrautarc  viin  uliam  corporis;  crgo  nc* 
que  modificare,        ]$*  N.  A*    Ad  Prob.  D.  A.  Diftan* 

«nequit  uUam  vim,  modificarc  jpen»«Ji/f79  caufa  fff,^ 
tu  C.  A,  pcrmodqm  fthmfii^  aut  termtni  N.  A.  dC 
I.  Ad  FrQb.  1.  D.  A.  Diftantia  nihil  cft  entifatis  ab^ 
Jiiutif  C.  A,  Nihil  ert  relatiouv  N.  A.  &  Cm,  Ad 
Prob.  II.  D.  A.  Diftantia  ncquit  immutarc  vim  ullam 
permodum  cauf^^  efficientis  C,  A.  pcrmodum  prmcip// ^ 
•ut  conditiouis  \}.  A.  &  Cm.  Si  brevius  te  cxpedire 
voles,  dieuo:  non  perdiftantlam  ifi  akftrnQo  ftmptam  , 
ied  per  difiantiam  ///  eoncreto  acceptam  determinari  cor- 
pus  ad  vim  rcpnlfiram,  (\vc  attra^ivam. 

V.  Ex  allatis  Pbamomcnis  ($.15  }  noncvincitor 
dari  in  corporibus  vim  rcpulfivam  ;  crgo.  Pr.  A.  Al- 
Jata  Phxnomcna  rcpeti  poflunt  vel  ab  effluviis  quibus- 
dam  avolantibus,  &  removcnribus  corpora,  in  qux  Tn- 
currunt ;  vel :  a  preflione  fluidi  cxterni ,  aeriSy  puta » 
aut  stheris  &c>  ergo.  9.  N«  A.  Nam  I.  tcmcrc  a^ 
iumuntur  effluvia  a  corporibus  avobntia,  &  removenti^ 
corpus  ,  iu  quod  incurrnnt ;  cur  cnim  (uberis  cfRuvia  rc« 
moveant  vinum,  &  aquam  ?  cur  non  fluida  qnsvis  % 
Dices :  Subcr  non  transmittit  vinum,  nec  aquam ,  quia 
minims  vini  moleculse,  aut  aquc  poros  ruheris  tranfirc 
nequeunt ;  hiiic  fit ,  ut  repellantur  vinum ,  &  aqua  ; 
non  q6ia  pcculiaris  quspiam  vis  rcpuifiva  iftud  opcrc- 
tur.  Crcdcrem  fortc,  fi  de  corporc  alio,  quod  itident 
aquam  non  tranfinittit ,  fermo  cflet ;  at  cum  de  fubere, 
liguomm  §mttium  prope  leviffttna^  proindequc  porq/lffifn0 
•gituc,  non  adducar,  ut  credam.  Deinde,  qua,  oro,  rft« 
lione  cvinci  poteft  ;  c.  c.  Mercurii  eflluvia  proportiona- 
ta  cflc  poris  auri,  vcl  ftanni ;  non  item  vitri,  V^el  ferri ,  • 
f  uibtts  rcpcUitor  mercnrius  ?    Qnomodo  vitrum  tranC 

C  4  roittit^ 


<v 


40  SgStoL  CaputlK 

^nittrt  effluvift  aqtKt»  nda  mercurii  ?  de  qtiibns  t«inen  ex* 
{fRnHlum  eft  i  fuhtUiora  ofTe  aquets.  2do  :  Qaod  de 
aere^  vel  «there  diclum^  eft,  refeliitar  ut  fupra  in  attr*- 
dlione.  Circa  atirufnqvie  nora  .  fi  cau&  n?ata«  fug« 
|it  aer^  vel  a^ther,  corpAra  (^usvts  (  modo  votQinine  =:  iui 
Siixti )  Fe^llentur  «(jqjatitei:;  non  attt^m  repteUuntiir  ;=t 
lueriergo. 

Vt  Quod  herbamm  a!iqu«  tangt  irRpatientes^^ 
ireri^,e.um^  qui  tangere  vult;  granula  fiia  (eminaliafll^ 
ciaitfy  repeti  poteft  a  caufis  mechanicia »  Qt  a"^  certa  dii^ 
f  ofitioAie  granulorum  ^  &  fblticuH »  ifuo  cointiB^ntuc  i 
crgo«  l^.  D*  A.  repett  potoft  ab  ilta.  difpofitianc  tan« 
quam  a  cau(a  r^rer^  occa/fomU  C>  A.  fojmoK^  &  cflicien- 
tc  hanc  granulorum  explofieuem  N^«A.  flc  Cm.  Stc 
bodiifr  exmima  c  ctiam  vi  repulGvae  ejfedas  iftc  tribacn- 
dias  efl^  de  quo  fortc  a!ta& 

Vifft  Insqtiilitas  attradionts^  vet  patius  minor  as« 
tra£Ho  .(  quam  aUi  negativam  dicunt  )  caufa  eflc  potcft 
phsenomenorum^quiat  vl  repuliinrat  tribuuntur  ]^  crgono» 
opusefl;  adflruercvim  rcputdvam  diflin£lam  a  vi  attra* 
fidva.  P«  A.  Dici  poteft^  quod  eorporis  aHeujus  rcpuNi 
partes  miituo  fe  trahant  magiSjj  quam  ab  alterius  cerpo* 
ris  partibus  trahantur.  Certc  metcnrti  partes  tnagis  (q 
ie  trahunt »  quam  a  tubls  capitkribus  trahantur ;  hihc 
xiuUa  in  iisdem  qicrcurii  afcenlio  notata  unquam  fuit ; 
crge.  "Bf,*  NT.  A.  Per  tnzquaUtatem  attradionis  cxpli* 
cari  nequeunt  vhhntijftnMt  ill«  cxplofiones»  quas  «quami 
inter^  &  ses  Itquatum  inrercederc  afTerui  (  §.•  I^* )  Ad 
Prob.  D.  A.  dici  idud  potctt  cirea  aUquaphsenomenaJn 
quibus  feiHcet  nulla  obfervatur  corporum  cxtraneorun« 
attraQio  C.  A.  tn  quibus  obfervatur  pofitiva  repulfiei 
N,  A.  &  Cm.  Quod  mercurius  in  tubo  vitreo  non  aN 
tollatur ,  caufa  ell»  quia  roajor  kabctur  attradio  in  par* 
tibus  mercurii  ad  fe  inviccm,  quan  qa»  efk  vitri  act 
mercurtum.  Sed  autem  \  qued  mercurius  in  tubo  vik 
tirto  non  modo  mn  attoSatt4f\  fed  deprimatur  ctiam,  qu« 

tiadcm  phsnomcm  iitiai  caofi  4i«i  ^otcrit  f  Fac  cnito^ 


\. 


r  I 

infunde  mereurlani  fiphoni ,  cujuf  cms  •leemm  >!t< 
iit  angnftius  :  in  crure  latiore  excelHor  erit  ^  qoimm 
•ngufto.  Immerge  tubultfs  mercurio  (bgnanti|  depri* 
metur  ille  intra  tubulos  infra  libellam  fere  in  ratione 
reciprocar  diamefrorum  Depreflio  ifta,  ceu  tffkBus  pofi- 
tivus  repeci  debet  a  vi  pofitiva  ;  non  ergo  repeti  poteft 
nh  aitra&ione  negativa.  Principium  iitud  pofitivum 
mihi  vif  ripulfiva  dicitur ;  datur  ergo  vis  repolfiva  a  ne<* 
gativa  attra4^ione  diftinCU^ 

VI 11.  Visr^pulfiva  non  diftinguitur  realirer  a  vt 
jtttradiva;  ergo  phsnomena  repulfionibus  tribui  folita 
repett  poflhnt  a'  minore  vi  attrat\iva»  ]$2.  D.  A,  Not| 
diflinguitur  rcaliter  abfolute  C.  A«  realittr  tftodaliter 
N.  A.  &  Cm.  Vires  attraaivat,  &  repuHivat  funt  di« 
'^verGe  modificationes  corperum ;  diflinguantur  ergo  ab 
invicem  mtt  tan^am  res  a  re\  ftd  tanquam  modus  rei 
«  modo. 

l!)(.  Saltem  ph^nomena  repolfionis  tribui  poflTunt 
csrentias  attraQionis ;  ergo  adhuc  vis  repnifivanon  eric 
vcra  vis  Pr.  A.  Ubi  ceilat  attra£^io,  incipit  fepulfio  ; 
crgo  repulfio  habetur  per  carentiam  attradionis ;  pro- 
sndeqae«  l^.  N,  A.  carentia  attra£lionis  eft  quid  ne- 
gativum;  i/f^ar/ v«m  autem  nequit  efle  effeSus  pofitivi 
frincipium.  Ad  Prob.  N.  A,  Pun8a  enim  in  iimitibvg 
cohsfionis  locata  qtiie(cunt,  nuliisque  ibi  vhribtis  ur- 
gentur,  non  attractivis ,  non  repulfiyis.  Dici  etiam  po« 
tefl  :  eeflknte  attraf^ione  incipere  repulfionem  hoe  (en* 
fxi  :■  quod  vis  attradiva  abeat  in  repulfivam  C.  A.  tan« 
'quam  fi  vis  repulfiva  fotet  nuda  carentiit  attroBiotiit  N«. 
A»  6c  Cm« 

X.  £x  didis  t  vis  attradiva  fiepe  abit  in  repuli!« 
yam ,  &  vicifllm  ;  ergo  hoc  ip(b  vis  repuHiva  confli« 
tuenda  eft  in  minore  attradione.  Pr.  C.  impercepti- 
btle  eft,  qua  ratioae  vis  artra^va  abeat  in  repulfivam  ; 
nifi  dicatur  2  yim  attradifam  in  certis  diftantiis  m«lfta« 
ri  quibusdam  gradibus  attractionis  (uc ;  ficq#  muleta« 
Pm  9blst  ia  vim  repulfivam  ;  argo^  ,    qt.  D«  A.  via 

C  {  «ttra. 


4JS  ScHio.l  CdjmtJT. 

«ttractiva  &pe  abit  in  rcpuliionem  hoc  (cnfii,  qitocl  ri« 
~  fuccedat  attractioni  C  A  quafi  repulfio  cilet  d<« 
tcrminatio,  fid  imnimuta^  ad  mutaum  accelittm  N*  ^. 
&  Coi'  Ad  Prob.  N*  A.  Hico  iiqo  t  per  minorem  at- 
tractionem  nihil  omnino  rcpulfionis  explicari ;  minc^r 
tttractio  adbocjeli  dcterminario  ad  mntuum  acceflum  i 
repulGo  6iftper  e(t  dctermioatio  ad  murutim  fugam,; 
qupmodo  vero  ^tuafuga  explicari  queat  fer  detcrtni* 
iMfionenB  ad  mutuum  accejjum  »  (atis  non  afleqqoc» 
Commodius,  puto ,  illa  yirium  attrahcnttum ,  &  rcpet* 
lentium  fucccflip  cxpiicatpr  pcr  varias  diftantias,  ita» 
ut  pro  rationc  variantium  diQantjarum  habcatur  vicilfi- 
tudo  attractionum»  &  rcpuI(ionun;i. 

XI*  Ncquit  in  corporibus  dari  viciflltudo  attractlp- 
tiom,  &  repuKionum  pro  raiiope  variantium  diftantia* 
rum  i  crgo  ncquit  in  corporibus  haberi  vis  repuliivf* 
Pr.  A.  (i  dccur  iila  viciflitudo,  failct  lcx  attraccionis , 
quod  vis  attractiva  agat  in  rationc  rcciproca  dopiicata 
diflantiarum ;  atqui  fallcre  non  poteit ;  crgo.  Pr,  M« 
In  miniinis  diftantiis  obiincbit  rcpuKio,  ac  proindc  fal- 
lct  lcx  attracrionis,  juxta  quam  hoc  major  dcbct  eflTe 
attracriOi,  quo  minqs  f fl:  quadratum  diflantis  a  corpore 
attrahcnte.  Kt.  N.  A.  Ad  Prob.  D.  M.  fallct  lcx  at« 
tracrionis  in  minimis  diflnnriis,  ad  quas  a  nobis  non  ex« 
tcnditur  C.  M.  in  majoribus  diflantiis  N.  M.  atqui  faU 
lcre  non  potcft  in  majoribus  fcilicet  diftantiis  C«  m.  in 
mtnimis  N.  m.  &  Cm«  Eodem  modo  rc(pondebis ,  fi 
dicetur :  Attractio  omnium  maxima  in  eodem  corpore 
cft,  fidiftantia  diszcroj  attractio  enim  cft  reciprocc 
vt  qoadratum  diftantidt.  Fal(a  eft  propofitio  prioic* 
Caafiklis  diftingoenda  ot  prios.  Item ,  cum  dicetuv  x  (i 
in  minimis  diftantiis  habetur  repoliio,  (cqoitur :  nultaoi 
baberx  attractionem  inter  corpora  minime  diftantia  ; 
quod  iterum  pugnat  cum  rccitata  lege.  Admitto  cnim 
fiqoelam  ;  nego  repugnantiam,  Satio  in  promptn 
fft.       • 

m 


% 


Lix  vhrlum.  4} 

XII.  Opponiint  aliqui  .*  In  co^m  febjttro  nc*^ 
^ueunt  effe  albedo,  &  nigredo  ;  ctlor  rummuSi  ^f^lS^ 
gus  rummum  ;  ncquc  igitur  ns  tttraetiva ,  &  rtpaifiva* 
Singula  bcc  in  codeni  fubjceto  habcri  pofltim  divcr* 
temporibus:  Dices :  Atqui  vis  repulfivt  ctdcm  tein* 
pore  conjungi  deberet  in  codcm  (ubjecto  etim.  vi  tttrt« 
ctiva  ;  dicitur  enjm  generalit  corponim  proprictti  non 
minus,  qnam  littractio;  trgo.  Jjf*  D.  m.  vis  rtpoUivt 
eum  attractiva  eodcm  ccmpore  conjungi  dcbcrce  in  eo- 
dera  fubjccto,  divcrfis  ttmen  fiibjeai  cjusdem  ptrtibus^ 
nt  patct  in  virga  claAica  ilexa  C.  mt  in  iiadem  materije 
partib.ns  Su6d,  fi  t0  vis  latc  fumatur  pro  powitia  C.  m. 
fi  pro  conatu  actualt  tcrminato  ad  idem  fubjeccum  iii 
cadem  diftantia  iocatum  N.  m,  ^  Cm.  In  eadem  anima 
eodem  temporc  habetur  facultas  volendi ,  &  nolendi. 
Idem  fit  dc  rc  noftrt.  $c4  jam  lcgcm  ipfinn  demon« 
Aro  : 

Demonftratio  Legis. 

§.  17.  ParS  Legis  Tma.   Vins  in  ukimit 

diftantiis /cfHper  fiifit  rs^lfiva.  Pr.  Nifi  vtres  in 
iiltimis  diftantiit  fint  repulfiv^r,  poterunt  cor- 
pora  quibuscunqae  velocitatibus  ad  fe  acce- 
aentia  pervenire  ad  immediatum  contadum 
fum  pTMdtntihus  vthcitatihus ;  atqui  non  pofZ 
funt }  ergo,  Pn  m,  Si  corpora  ad  immedia«  - 
tum  contaftum  perveniunt  cum  praecedenti* 
bu$  velocitatibusi  Compenetrabuntur^vel  cert^ 
^abitur  ialtus  in  rerum  natura.  Neutrum  fii« 
ftineri  poteft  (  $«  1 1 .  &  i  a, } ;  ergo,  Pr.  M* 
£x  legibus  motus»  &  experientia  certum  eft » 
Corpora  duo  non  elaftica  in  iefe  incurrentift 
poft  coftftiaum  s  li  celeritatt  ferri.      Hoe 

pofi. 


44  SeHio  T.  CapuiTf. 

^M^m !  concipumtut  duo  cerpora  aquBlh  ( fcribit 
^BOTfcovichius  )  ^ua  moveantur  in  direBum  verfuf 
€andem  pUgam ;  (f  id  ^  quod  pracedit,  habeat  gr^ 
duf  velocitatis  6 ;  id  vero^  quod  ipfum  perfequitur  ^ 
gradus  1 2.  Si  hoc  pofterius  eum  fua  iUa  veloeitata 
tUafa  deveniat  ad  immcdiaeum  contaBum  cum  iU§ 
priore »  aportebit  uti^ue »  ut  ipji  momento  tcmporis  ^ 
^fuo  ad  cofStaSum  devcnerint ,  iUud  pofterius  mi» 
nuat  velocitatem  fuam ,  £^  iUud  prius  juam  augeat , 
utrumquc per  faltum  :  a^eunte  hoc  a  it  ad  ^  :  iU 
h  a  6  ad  9  ftnc  uUo  tranRtu  per  intermedios  gradus 
II,  Sf  7;  10,  £?'  8  £5^.  iftquc  enim  fieri  poteft^ 
ut  per  aliquam  utcunque  exiguam  continui  temporif 
fartieulam  ejusmodi  mutatio  fiat  per  intermediot 
gradus  durantc  contaHu.  Si  enim  aliquando  sdti» 
rum  eorpus  jam  habuit  y  gradus  vehcitatis  ^  t5  aU 
Urumadhuc  retinel  II  ,  toto  iUo  tempufeulo  ,  quoJ 
efiluxit  ab  initio  contaStus ,  quando  velocitates  erant 
12  >  5^  6j  ad  id  tempus^  quo  funt  '11 ,  Hf  7  ^ 
corpus  2dum  dehuit  moveri  eum  velocitate  majoro  ^ 
quam  i  mum ;  adeoque  plus  percurrere  fpatii^  quana 
iUud ;  £f  proinde  anterior  ejus  fisperficies  aebuit 
tranfcurrere  ultra  iUius  pofteriorem  juperficiem ,  if 
idcirco  pars  aliqua  corporis  fequentis  cum  aliqua  an-» 
tecedentis  corporis  parte  cotnpenetrari  debuit ;  quoi 
cum  ob  impenetrabilitatem  fieri  omnino  non  pojfit  ; 
0portuit  fanCf  in  ipfo  primo  initio  contaHus  mutatia 
vehcitatum  faSia  fuerit  per  faltum  fine  tranfitu 
fer  intermedias }  ergo  fi  corpora  ttd  ifnraeaia« 
fum  contaAum  perveniunt  cum  pr«ceaentN 
Inis  Velocitatibus ,  compenetrabuntur  ^  vel 
Ctrce  dabitttr  ialcus  tn  natura.    Qsiod  fieri 

'  cum 


Lixvirtum.  4]$ 

etim  nequedt ,  clebet  snu  cmt^mn  immidu^ 
tum  graJatm  in  aliqua  dift^ntia  exftingui 
locitas  corporis  accedehtis  ;  debet  ergo  dari 
vis  aliqua  illam  e^cilingiiens,  ac  proinde  agtns 
dirUiione  oppofita  (  ii  ehim  agatdiredione  con- 
^irante,  augebit  pocius  veiocitatem  corpo- 
ris  con(equentis  »  quam  imminuat)  •  Siquo 
agit  MnSione  oppofiu  »  nititur  a  ik  removm^ 
corpus.  Vis  y  qaas  corpus  aliud  a  ft  removere 
iiititur ,  repulfiva  eft ;  ergo.  Dixi :  Vtres  im 
ultimis  difimtiis^  femper  funt  repuKivas ;  nam  . 
in  aliis  diftantiis  non  obfervamus  imminui  ve-- 
locitatem  corports  accedentis ;  ne^ue  habetur 
ratio  fufficiens  ejusdem  in  aliis^  diftanciis  mU 
suendae;  debet  ergo  imminui  in  ultimis* 

CorelL^L  Non  modo  rim  eerperum  in  ulti|iii$  di* 
fianciif  (emper  (unt  repulfivflr ,  (ed  etiam  vires  fuu^o^ 
rum  elenmitarium  ;   nam  ii  in  illis  diftantiis  non.  fine  « 
refpulfivae,  compenetrabuntur.     Veritas  amplius  pa^ebit 
«xCoroU.III. 

CoroU»  IL  Corpera  ad  immediatum  eontaSim  wmU 
reJtfer  perveiUre  nequemt,  Pri  Vircs  coaporum  in  uU 
timis  diftatuiis  icmper  (unt  repulfiv«  >  he^  eft  s  remo* 
rent  corpus  accedens;  atqui  fi  illud  removcnt^  non 
pofliint  corpora  tc  fe  immediate  pontingerc  ;  crgo» 
Pr.  sdo;  Duo  e.  c«  globi  moti  in  eadem  linca  rccu^ 
&vcrfiis  candcm  plagam^  quorumalter  prsccdat  ce^ 
lcntate  ut  6 ,  alccr  in(cquatuc  cclcritatc  ut  i  a ,  non 
poffunc  namraliccr  cd  immcdiatumconttcnun  jpcrvcni* 
Tc;  (ectt8ip(b  momcnto  contaetia  cd^ritas  corum  muh 
trf>itur  pcr  ftitum  tranicundo  jus^ta  kgcs  motus  a  celc« 
ritatc  ut  6  ad  cclcntatcm  ut  9  ;  vcl  fi  maCttur  grada» 
$im,  compcnctf abumur )  quod  oftcnde:  fi  cnim  ce)c« 
mvf  tefi  eemaSum^  vc\  i(g/c  maimm  ,^!»n^^  grad^» 


46^  SeOioL  (UputlT. 

iBll^r  majorc  celeritttc  fcrctur ,  qoam  prior ;  imm  fi 
prior  acquirit  ccleritatcm  ut  7 «  poftersor  adhuc  habct 
IX  ccleritatis  gradus  ;  fiquc  prior  ilic  acquirifg,  rcti- 
tiet  poftcrior  10  &c. ;  crgo  pofterior  fo/i  conta&um  in 
gadenijinea  reSa  plus  fpatii  conficit,  quam  prior;  quod 
abfquc  compenerrarionc  ficri  nequir. 

CeroU.lth  EtiampUHth.  eievtiutaria  fe  fe  namra^ 
Ueer  immediau  coutingere  ttefueuut;  nam  cum  punct» 
hcc  iim  fimplicia,  adcoquc  incxten&^  &  partibua  defti* 
tpta^^ncqtieunt  (ccundum  partem  aliquam  Ce  contingerc, 
N  &  (ecundum  aiiam  non  eontingerc  ;  fique  Ce  mutuo 
contingerent ,  omuino  compettetrarentur  ^  quod  viribut 
tiatura:  ficri  nequaquam  poflTc ,  iatis  jam  dictum  cft. 
Rcete  inquit  Boskovicbim :  J^i  ipfi  vim  iuferat ,  oportet^ 
qut  fuuBum  pundo  coutiguum  coucipiat ,  &r  tamen  extra 
ipjum  ,poJ!tumyUec  comptfutratum.  Otncipit  globulot  quos^ 
dam  extenfos^  quigloiuli  cx  una  parte  fe  contingant  ^  ex 
stlia  afe  invicem  recedant\  ubi  partet  ejusdem  pun&i  ad» 
ffjittet )  y  indivifibiiitatis ,  ac  extenjtonif  ideam  deflmet. 

•  lEfl  id  fatii  vetufliffitmtm  argtmentum ,  quo  fetnptr  Zeno» 
nis  fententia^coHtiuuum  extenjuiri  componentis  ex  pUflQie 
ptnitus  inextenfu^  confutata  efl  ^  ettjtss  folutionem  aptam 
nehto  tutufqua  exiibetra  fotuit ,  nema  profeSo  exbibebit 
inpoflertm ,  dwi  stbfihttifftma  detttonflratiouis  ,  s  qtt$ 
evideutise  vim  babut.  Pr.  tdo  :  Si  non  corpora  f 
Hequc  puncta  clcmcnttria  immcdtatc  (e  cohtingere  po* 
terunt,  &  viciflim  i  tcomactua  enim  corporum  alitef 
liaberi  noii  poteft,  qoam  ^natcnus  puncta  corpus  unum 
componentia  immcdiatc  cbntingerentur  *  puiictis  tw 
pns  alt^nim  compoooitibus ,  qwa  corpns  alterum  cate* 
nns  conttngerttur  ab  altero ,  quatanua  fiihftantia  uniui 
contingcrctur  a  fiibftantta  aircrtut  { nequc  enim  aCei* 
dcntifl  corporum  Ce  contingunt ,  cum  fint  modi  fiib» 
ftantiarum.  Dabo  imo  acci(kntia  (c  eontingerc,(ed  infc» 
rttn  continuo :  hoc  i^lb  ftcomingttnt  fiibftantis,  qoarunt 

.    fiint  ffiodifiQtMnta ) ;  trgo  mim  ia  corporftus  nthtl  fic 

fiib- 


AMhmi^  pratcf  entia  fimplicii  (  per  iieutpbyficam\  ^ 
Cbrpora  (e  contingere  non  poiTuQt,  ni(i  (ecundum  M0Sr 
finrplicia ;  proinde* 

X  Schcl.  Ftdelirer  primnm  confignabo^  quc  adirefius 
fonc  pofitionem  plerumque  objici  notatut  Bostovkhim\ 
ttim  aiia  rubjiclam.  I.  Si  corpora  ad  iimnediatum  con- 
tftctum  pervenire  non  pofTent ,  tum  ideo  ,  quia  compe* 

/fctrarentur ,  vel  certe  daretur  fiiltus  in  natura  ;  atqui 
*  iftud^^penes  corpora  actu  exiftentia  nen  (equerctur  % 
^£,0»  Pf .  m.  dicta  compcnetratio^  vel  fiiltus  in  natura 
icqueretur  tantum,  fi  corpora  perftcte  dura ,  que  nimi* 
^tm  nullaih  cotrpreflionem  (entiunt,  6c  nullam  iigurje 
mutationem  induci  patiuntur ,  (c  fe  immediate  conttn« 
gant|  npn  vero  ficorpora  elaftica;  ergo  cum  corpora  per* 
fecte  dura  a  plurimis  Philofopbis  exdudantur  a  natura, 
iftud  penes  corpora  actu  exiftentia  non  6queretur,. 
Pr.  m.  dnm  le  corpora  eia(tica  contingerent,  fieret  /»« 
/roceJJUne,  &  cBmpreffione  partiiim,  ut  dum  inttrea  cor« 
J^orls  tompredi  ligura  mutator  (enfim,  in  ipfis  corpori« 
bus  etiam  relocitas  immutetnr  (enfim  ,  ac  fine  (altu  » 
ttanfeundo  per  omnes  intermedios  gradus ;  ergo  dicta 
compenetratio,  vel  (altus  non  (equeretur  penes  eorport 

*  flcto  exiftentia,  qux  ob  elafticitatem  fi)ara  introcelfionis^ 
&  comprefiioms  partium  utique  (iint  capacia.  ]^» 
C.  M.  N.  m.  Ad  Prob.  N.  A.  Ad  ulteriorem  Prob. 
t>»  A»  fieret  iftud  ,  ac  proinde  vitarerur  (altus ;  non  ta* 
ntiH  vitarerur  compeitctratio  ^  T.  A.  vitaretur  utrumque^ 
N.  A.  &  Cm.    Partes  quidem  prsrcedentis  e.  c.  giobi  '* 

Softeriores,  &  in(eqnentis  anteriores  comprimerentur^ 
mfimqoe  fibi  cederent ;  (ed  hoc  ipfb  anteriores  globi 
inreqoehtis  partes  moverentur  tentius,  quam  poKerioret 
ijusdem  globi ;  quodrca  iftae  plus  (patit  conficere  debe- 
rent  pr«  illis  in  eadem  linea  recta ,  Ql  cadem  directio* 
ile  motis  ;  ac  proinde  compenetrarentur.  tjL^  odo» 
K^A.  Prima,  &  ultima  fiiperficies  corporum  (e  immc* 
diate  contingentitim  dcberent  mutare  velocitatem  pef 

filttuni  fi  e«  ad  immediatum  contactam  piervenireiif 

/  i  


mm 


4%  StBhh.  Cspuin. 

enm  praeeJemthti  velMmihm ;  mox  cnim  poft  con* 
VHii^  moverentar  ccieriute  s  li  \  aut  vero ,  ii  ins* 
quah  :  compcnetrarentury  quia^  infcquentis  corporis  (u« 
pcrficics  «ntcrior  plns  (patii  dccurrerc  deberet ,  quani 
prcccdcntis  poAcrior»  Colliges  facilC)  cur  fupcrius  di* 
xcrim  T.A.  $tio  «  T.A.  ob  dicta.  D.  C.  dicta  com« 
penetratio»  vei  faltus  non  (cquerctor  forte  pencs  corpo* 
n  actu  cxidcntia  (  qulod  tamcn  falfum  e(t  )  (cquerctoc 
tan^cii  altcrntram  feiics  fuuQa  elemeutaria  C.  C.  non  *' 
fcqocrctur  N.  Cm.  NcutonuS)  plcriquc  imo  vctc* 
cum  ctiam  Philofbpliorum  prima  eicmcnta  materijiK 
omniiio  dnra  admittunt  cum  impoflibilitatc  abfoiuu 
mutandi  figuram. 

II.  Etiam  »  fi  ^ncta  clcmcntarta  (e  immcdiato 
contitigcrcnty  ccicritas  non  m^tarcthr  pcr  (attam;  cr* 
go«  P.  A»  ibi  cclcritas  non  mutatur  pcr  (aitom ,  nbi 
nuiia  habctor  quantitas  motus ;  &d  in  punctis  clcmcn* 
taribus  nullc  iia^etur  >'  crgo.  P.  m.  Motus  ^  juxta  Mc* 
chanicos  habet  pro  mcnfura  madam  ductam  in  ceicri« 
tatem ;  mada  autem  tfk  (uperficies  bafeos  ducta  in  alti« 
Itiidincm  e.  c.  in  prifmatis.  Puncta  cicmentaria  ncc  baiim 
babcnt,  nec  aititudinemv;  (imilitcr  crgo  non  habenc* 
tquantitatcm  motus.  4^.  N*  A.  ad  Proo*  C.  M.  N«  m« 
adhujus  Prob.  D.  imam  partem  A.  ;  Motos  corpQrurm 
habct  pro  mcnfiira  maflam  ductam  i|i  celeritatem  C^ 
hanc  partcni.  Motus  tkmeHtorum  Suhdifi,  ri  m^jjk 
fiimcndo  pro  ip(a  eicmcnti  fubftantia  C.  hanc  panem  i^ 
wo  coiicctionc  (iibfiautiarom )  aut  «Ho  quocunque  (en* 
hnnc  partcm,  D.  ctiam  sdam.  MalTa  impropriO 
fiimpta  pro  mok.^  (ea  volumine  eil  rupcrficies  bafeoa 
ducia  in  aititadincm  C«  h.  p%  in  rigorc  fumpta)  ut  (iiml 
dcbcc  N«h«:p.  f^olumeu  dicitur  totum  iftud  fpatium  ^ 
quod  (ttb  cxtema  Corporis  fuperiicie  continctur  ;  aut 
dipcrficics  ba&os  dacta  in  aititudinem  c.  c.  priCinatis  i 
iu>n  me^*  Certc  plus  malTjE  eft  in  pedc  i;ubico  aurl^ 
<)U9fn  In  pcdc  cuI)ico  iigni^  iicet  utrobique  fupcrHcid 

m&u  dttcta  ia  akitudtoeffii  6c  aisUi»»      fmtm  )ttatii 

ftd* 


,  pro  c€ 
Ei  N. 


Lex  virium.  •  49 . 

tdmitto;  ftd  D.  C.  crgo  nqn  hahcne  quzutitsntmjfm*^ 
tus  convcnicntcin  corporibiis  C.  C«  iibi  propriam  N.  C* 
Meclianici  ipfi  inotutn  tribuunt  Safiiferficiehus,  &  Uueis^ 
&  fun&is^    Phyfici  omnes  nmum  ceutri  gravUatis  %Qx* 
idao  nominant. 

111«  Senttntia  ncgans  immdiatum  corperum  contOm 
^Bum  zd7cr{ktur  communi  hominum  opinioni;  ergo  rew 
jicienda  e(l.  ^.  D.  A.  adverfatur  communi  bominatll 
opinioni  in  prsjudiciis  infandd?)  &  tedimoniis  lcnfuugi 
iFiindats  C.  A.  fundatx  in  folida  ,ratione  N.  A.  &  Cm»  ^ 
Primum :  eO:  hsc  opinio  prsjudicata  ab  infantia,  in  qua 
{>ierumque  tlTendim  przbere  (blet  tenera  ctas  iis  rebus  ^ 
tqux  ab  adultioribus  recenfencur,  aut  quorum  ideas  ipGi 
(ibi  efFormayit»  Prxcipiratis  id  genus  judiciis  >  altequo 
animo  infixis,  quin  vcritas  afliJuo  prius  examinarctur^ 
Seriamat)  qt  viri^  ^c  iines  pertinaciter  tueantur ,  qu« 
olim  juvenes  prscipitancer  cogirarunt.  Slc  plane  (e  res 
hflbec  in  prxCctxd  4e  immediutd  corporum  contMdu  coa* 
itrovcrna.  Dices  3  Omnes  homines  per  tot  annoruai 
&euia  judicium  prxcipir^verirjt  ^  nemo  unusjudicii  ve>» 
ritatem  inquifterit  |  nemo  falfitatcm  agnitam  ingenuc 
confedus  fuerit  ?  Dolenter  ajo  :  /otnnes^  itemo*  Sicut 
iomfies  ad  Cofernicum  ufijue  (  urinam  non  hac  state  nO<» 
Ara  )  judtcia  prscipitarunt  tircd  motum  fotis ,  &  quie^ 
tem  tetrx  ,  nemoque  (ytteroatis  hujus  veritatem  \sk  dii^ 
bium  vocavit ;  fic  ncquc  contaaumk  Jam  reliqunm  eft^ 
otprobem  :  opinionem  advcrfariornm  mak  fundari  ia 
u/iimeHi^  fefifuum,  Senfibus  fiibdacuntur  minimet  di'» 
fiantta  :  (ttbducuntur  corporum  plurimorum  pori^quoi^ 
«amen  corporibus  omnihm  inefle  (uadtt  anal^ica  ratia 
defum^td  a  plerisque  ahis  corporifous  ^  quorum  poroii» 
tatem  evincunt  imo  t  diverfa  gravltas  ^^  todemv^lu* 
n(tke^  h.  e.  diver(a  gravitas  y^^^ca ;  ado  t  tr^nsmiffio 
iluidorum  ^  (airem  iuas^  &  caicrif^  fi  o»rpora  in  tennef 
^  bra^eas  diducantur.  ^tio  1  Microfcopia.  Ergo^  cum 
fHimma  di/kntiif  |  in  quibnt  \iipcrtitur  vis  irepulhva,  (uli« 


50  Sf^l  Caputir. 

^^icur  {enfibas,  pro  immediato  contaSu  corporum  1#* 
gitifnam  teftimonium  a  (enHbufi  repeti  nequi^ 

IV.  Sententit  negans  conta^m  corporum  adverfi- 
tur  prudenti  oinnium  hominum  opinioni  ,*   ergo  ctiam 
fententia  negans  immediatum  contahum  corporom.     Pr« 
C.  Conta£tus  prim^va ,  &  fincera  itgnification^  (ua  ac-* 
ceptus  denotit  immediatum  conta&um  ;  ergo.      tf,.  D* 
A.  Sententia  negans  conta&um  apparentemy  6l   PbyficuTfi^ 
adverfiitur  prudenti  homindm  opinioni  C  A.    conta* 
dlum   immediatum  ,    &  Matbematitum  N.  A.  &  Cm. 
Non  negainus  corpus  alterum  ^b  altero  contingi  Phyfi» 
ce^  &  ad  (endim  ^  ladeoque  mediate ,  mediantibns  (cilicet 
minimis  illis  intervallis^  qux  (enfibus  (ubducuntnr.     At 
immediatum  contadum  omnino  exclttdimuSi  de  quo  ni- 
hil  nnqnam  conilitui  poteft  dependenter  ^  fenJSfUS.     Ad 
Prob.  N.  A.      T^  conta£tus  cx  primxva  iignificatione 
fua ,  &  inHiitutione  hominum  fignificat  contadom  dun« 
taxat  Fhyficum^  &  appareutem^  non  verum^  immediatum^ 
&  Matbematictwh  .      In  vocum  inftitutiont  babenda 
etiam  fuit  ratio  vulgii  quod  Gepe  exiiliinat  noi>inulia 
cfTe,  qu2  non  funt ,  ut  ex  adverfe  putat  non  etTe ,  qux 
revera  (iint.     Ad  Mathematicum  contadum  non  fe  ex* 
tendit  hominum  vulgus,  imo  neque  olim  Philoiopbi. 

V.  Si  corpora  (e  duntaxat  Phyiice  )  &  apparezitet 
contingunt,  non  iiximediate,  &  reaUttr :  atmquam  parc* 
rit  corpus  unum  impelli.  ab  ahero,  t^ut  dereroiinari  qua* 
cunque  alia  ratiooc  admot&m  ;  atqui  poteit ;  ergo. 
Pr.  M«  Si  pofiit :  communicatio  motus  iieri  dcbebit  per 
vacQum  \  atqui  non  poteft ;  ergt.  Pr.  m»  Ad  omneni 
commnnicationem  requiritur  coutiguitas  tanquata  con- 
ditio ;  quis  ealm  commiuiiccr  motum  globo ,  qutm 
pon  oontingit?  ergo.  *^  N.  M.  ad  Prob.  C  M^ 
N.  m.  aduit.ffrobu  D.  A.  reqiujrituf  comigoiut  iaiicoi 
appar-ins  T.  A.  fM  imiveriaUter  iallir  profM>0iiOj  ut  pa» 
tet  in  magnete  uAtnic  fercam  fibi  noo  contignum* 
€$ntiguim.  vkM ,  &  sfsiM&M  N«  A|  ^  Cnu    Si  uiiamt 

iiU     ^ 


Lcx  viriufh.  H^ 

i^a  coittiguitas  inteiligitar ,  vitium  eft  in  argumeiftatid* 
ne  ,  (cilicet  fetitio  fr'tncipii\  iftud  eniip  ipfum  efl-,  quod 
quflcritur.  Cxrerum  ,  qui  prsjhdicils  eliberatus  '<A 
(qualisefTe  debet  Pliilofi^phus  omnis  )  facile  a()vertet^ 
tiihil  cotttiguitat$m  conferre  ad  communicationem  mo« 
tus  ,  tum  quod  contiguitas  de  fe  adiva  non  lit ,  heque 
vim  ullam  habeat;  tum  quod  communicatio  motul  non 
fit  per  aliquam  triinslationem ,  aut  transfnfionem  ex  cor<» 

Sore  uno  in  aliud  {  abfit  figmentum  )  ,  fed  per  hudafti 
eterminationem  cum  aliqua  virium  jafiura. 

VI»  Nulla  tnotus  communitttib  >  impuliio,  aut  de« 
terminatio  fieri  pot^ft  fer  rem  Mi  exi/knttm ;  ergo  ne* 
qat  per  vacuufn»  ^.  D.  A.  id  eft  t  a  re  non  exiften* 
fb  C.  A.  quafi  int^r  corpus  impeilens ,  <St  impQlfum  » 
^u(am  inter,  &  effefiom  efle  d^beat  ens  aliquod  inteN 
medium,  quod  iit  ceu  vehiculum  a£lionis  N.  A.  &  Cm. 
Mbfi  entU,  aui  nibili  HuUafuHt  proprietates,  if  affeBionet, 
^rimnm  eft  axioma  KeiSii ;  erg;^  etiam  nalls  ihnt  vi- 
res,  nuUsr  adiones.  KegatO  immediato  comaAu  cw- 
)>oram  adhuc  corpora  manent  entia;  ergo  adhae  lo 
Inutuo  impelltre ,  inque  fe  £e  ageik  p#terunt. 

VIL  Si  corpora  (e  immediate  non  contingunt,  fequt* 
jtnr  I,  quod  baculo  vehementer  vibrato  perculTus  nihil 
fentiat;  (emper  enith  diftabit  baculus  a  corpore,  in 
quod  impreffio  faciehda  eflet.  Addunt  adverfarii  noftri 
I)umani£umi  :  baculo  utendum  efle  ad  perfnadendum 
contadtun  neganti.  II.  quod  nulla  unqUam  haberetur 
lenlatio  ;  organa  enim  ftnforia  ab  obie£^is  {enlibilibui 
nunqua^n  afticerentur,  &  immutarcntur,  quia  nunquam 
contingerentor.  III.  quod  uvie  in  torculari  nOn  com* 
primantttr.  IV.  quod  kieos  a  malleo ,  accium  muri,  ^ 
moenia  a  globis  non  verbcrehtur.  V.  quod  cuitro  ^Cu. 
ftum  e.  c.  ligni,vel  panis  &c.  noh  difcindatur,  ftdqtUI 
prius  cohcferant  partes ,  (ponte  velmi  fua  diflbcieiitttf. 
tixe,  &  plurima  alia  horum  iimilia  (cqui  necefle  eft. 
'^.  ad  1«  Nl  (equclf  ahnexam  caufil^di  D.  tktafet  enlm 

D  1  bacjnp 


$2     r  SeBiot  CaputlL 

^lHifl^us  dlAabic  a  corporc  diflantia  Ahtiemfitica ),  b.  e« 
tton  continget  corpas  imfnttdiate^   &  Matheviatice  C* 
Diflantia  Tbyjica^  itjr,  ut  corpus  ncquc  contingat  media^ 
te,  S^Fbyfice  N.     Pofito  contaftu  Phyfico  jam  imprefli^ 
in  corpus  fieri  poteft ,   lion  fecus  atque  admifTo  coiU4« 
fiu  Mathematico  ;    quid    cnim    conta6lus   itninediatus 
conferat  ad  imprcflionem  faciendtm ,  citm  nihil  fit  a^U 
vi?    Dices:  nihil  omnino  cft  tdliyi ;  at  eft  conditto  adi 
imprcffionem  faciendam.      J^.  iterum  :  htcc  manifcfta 
cft  fetitio  frineipiiy  dc  hoc  enim  quffritni'.      Quod  ad* 
verfarii  pro  liherali  humanitate  fua  per  jocum  adduitt 
de  perfuafione  a  hacijh  repetenda ,  nihil  moror,     Priut 
.Camen,  quara  in  nobiPpcr  jocum,  in  fe  ipfis  Caio  expe» 
riantur^  an  non  ipfi  utcunqRe  tunicati  acerbe  dolebunt^ 
a  baculus  dextre  vibratus  uon  quidem  corpora  eorum^ 
ied  tunicam  immediate  continget.     DoIebunt6ne  ;  at» 
qne  utinam  doleant  ad  corre6tionem,ad  ponenda  prsejii» 
dicia.      Credo  ego,^ii  pofitis  praejudiciis  inteliigcrent 
Vim   repulfivam  iu  ultimis  diflantiis   agentem  eosdciii 
motus  excirare  pbfTe  in  organis  fenfbriis,  quos  corpor» 
in  contaOu :  eadcmque  prorfus  Phanomeiu  eventura^cflct 
negato  couta^u  imn^diato,  qua?  admijfo ,  non  adeo  tena* 
ccs  efTent  ppinienis  fiis»        Ad  il.  N«  fequel.  Organa 
(enfbria  rcvera  afficerentur,  &  immutarcntnr»     Fis  re^ 
pulfiva  oVje&i  fenfibilis.eandem  mutationem  induceret 
in  fibras  Organorum,  quam  contadlus  ;   hsc  organorum 
impulfio  sque  per  nervos  propagaretur  ufque  ad  cere* 
brum,  qux  fedes  eft  anims  ;  anima  ex  l^ge  commercit 
perinde  adverteret  ad  motus  fibriljnrum,  &  aglcationelli 
cerebri,  atque  alias.     Ad  III.  &  iV«  ajo  :  <k  uvse  in  tor« 
culari  comprimuntur,  &c  incus  a  malleo,  &  arcium  mu« 
ri  a  globis  verberantur  ;   fcd  fine  immediato  coistaClui 
Vt  cjusmodi  cfFcftus  habeantor ,  fufficit  tontaStus  thyfim 
cus  j  fufficlt  ncmpe  corpora  locari  in  diftantiis ,  in  qufw 
bus  vis  rcpulfiva  cffeftus  illos  opcwri  qucat.      Ad  V. 
D.  A.  quod  cultro  fruftum  e.  c.  panis  non  difcindatufg 

cuitrv  rciUcet  ai  immidiamm  cmaOum  dflM  C.  A^ 

aA 


lexviriuffi»  53 

ad  eontaSum  mediattim,  &  Fl^ficum  N.  A.  &  Cm.  Vh 
rcpulfiva  cuitri  facft ,  ut,  qu«  prius  cohacftrant  partci* 
panisy  appHcito  fubindc  cultro  diflbcicntur,  nontameii 
qitafi  fponte  fita ,  quod  innucbat  objcftiot  Hic  cgo  bo« 
jios  advcrftrios  ireruni,  itcrumque  majorem  in  modunt 
obtcftor,  uti  animo  prxjudiciis  vacuo  difpiciant,  quantft 
facilitatc  negato  contaSiu  immediato  Phsnomena  quocque 
,  wpliccntur.  Eadcm  (anc ,  qua  in  fententia  oppofita  ; 
forrc  ctiara  majore.  Scd  cnim  :  an  «quc  fclicitcr  ad« 
ver&rii  rariones  a  nobis  allatas  (  §.  17-  Coroll,  ado.& 
3tio  )  difTolvant ,  arbitrio  virorum  prjtjudiciis  non  0CCU« 
patorum  lubcns  rclinquo, 

Corott,  IV.  Corpora  omniafunt  porofa.  ?toh$ 
Qusvis  punfta  clemcntaria,  &  particulaB  minimsc  corpus 
conftitucntcs  fc  (c  in  ultimis  diftantiis  repcllunt  ita ,  ut 
ad  immediatum  contafluin  pervcnire  nequcant  (  |»^7» 
Coroi!.  tdo  &  ^tio);  crgo  inter  minimas  corporuin 
•fndcculas,  &  ipfii  adco  punSa  intercflc  debent  inter- 
vaHa  quspiam  vacua,  quibus  a  fc  disjungantur»  £ju5- 
inodi  intervalla  partibus  (blidis  interje£ta ,  &  materia 
fropria  corporJs,  in  quo  habtntur,  deftituta  porot  dict« 
mus ;  crgo  qusvis  corpora  habent  poros,  Dixi :  m- 
tervalla  materia  propria  corporls  dcftituta  pori  fimt ; 
non  tanquam  fi  in  mcatibns  illis  corpcffunr,  fivc  iutcr- 
vaJIis,  &  vacuoiis  nulla  habcri  debcat  materia.  aliena, 
c.  Cr  /«c^,  aeruy  cetheris  &c.^  fed  quod  fufficiat  non  tdeC 
€t  mareriam  propriam  corporls,  cujus  fnnt  pori.  Pr. 
11.  Microfcopia ,  tranfmijfio  fluidorum  (  faltcm  lucfs ,  fic 
aalorif )  denique  diverfa  gravitas  fpecifica,  (cu  divcrfiim 
pondus  corporum  fub  eodem  vohimine  manifcftc  win- 
cunt  in  corporibus  dari  poros.  Sic  in  plantis,  lignit» 
©(Tibus,  pilis,  &  rcnuibus  quorumiris  metallorufn  bra-. 
Acis  innuracraWlis  pprorum  muititudo  confpicitur. 
Corpora  omnia  in  t^v^cs  lamcUas  diduAa  caUfieri^  lu* 
cemque  traufmiture  poffunt.  Plerajue  corpora  nativ« 
hm  indoli  rcUft»  vtrios  liqtiorcs,  &  «uida  in  fc  roci* 

D  l  twtt^* 


1 


f4  SeSlhL  Gipmir. 

T^nu  AddacQ.  p«uQi  t  auram,  acgeiUfiCD,  ftatmins  AKa 
pjerineantar  i  mercorio.  Claufia  oculia,  manuque  in« 
terje^a  Qspe  advercimns  coru(c$tio9e$  ^  aut  lucem  ^ 
^le,  veL  candeia  propi^i/atn*  De  abfumptis  24.  horaruni 
^atioo^o  iibria  qMmvi^ per  tKau^ira^i(^ifitfti  abiifle  depre^* 
henfuizi  t&%  Aturnalia  qusquc  aftate  langaeTcaut ,  aQ 
4eficiunit.  (^ua  caufa  ?  qQiat  ca/arf  i^/vo  l^antta  pori. 
f^  proinde  habetur  mijoj;  tr^Q)ir^tio,  Marmor  d«ri4 
!HO],um|^  ^chatcs,  itejQ  chaJcedonii,  ^anmm  &e,  tam  a£i  ^ 
4ibi;o  tingi  foiqn^  fi>lati»nc  argcnti  U^  iiv  (piritn  nitri^ 
^ddita  oOiOi^LaQqa^px  fuligine  ^  taruro^  rubro,  vcl  alumi* 
ne  piumofo  &ey  ut  a()  ipit^  njttura  expi^A  credanxui^ 
(  (ed  ritium  detegitur  admoto.  igne,  yel  aiTu(a  aqua  for^ 
tl}.,  A<|aii,  ab  ^tt  o^purgata,  in  (c  aprcqi  admittit 
r^  ofifip,  v.Qfumif^:K  ^piritus  xUii,  dc  iiqua  (i.  pomdii^ 
«ptntuCx  i^i^us  voiumAKk  OCqnip^bunt  mixtaj^  quam  fepa^ 
]^a*.  Si  vitrep,  cy^i^Ot  c%vo,  ^y^xnq  aggiutinctui; 
iiiginentJ^n  fpba^ricun^.  lignecvn  utpujEique  crafTum. ,  aa 
di)rHm,  (c4  itidcm.  e3|^ca|ratum ,  ii>  cujua,  cayitatem  inu 
mittaiur  iive  aqua,  (ivc  mcrcudQS :  dein.  xcro,  ope  Antlia^ 
Bnevjwtica;  ex  cylindrp^  xitreo,  aer  extrahatur  :  fie^ 
jm^JJiot^e^  aeris  extemi\  ut  flpidum  (egn;iepto,  contentumv 
infta^'  t^ntiis.  pluvix  intri^  yitrum,  dqcida^*  Nuoqui^ 
j^f.  ppco<.  ligni  ?  Si  prp,  cainp«na»  iMti^^fl(  ad.  patinaini 

'  liacijffr  apponi  (liiit;^  ap^natui?  yas  ligjacunTi  aerc  eva^ 
cp<y[i4um,  nunquaxn.  pjcejjiipni.  ai^ris  exiterui  ijirmiter  adn 
ha(i;^it  patin^,  quia.  nunq.pam.  oq;ii|inp  acr  ^xhaprietur^ 
Cpc  y^«^o.?'  firiJ.icet  aer  fer^porojiiigni  higred^ens,  (cmpecv 
<;pm.ilipoJ.cabit  cam.  ex;ernp ,  t^  pi^oiode  tantum  jreiiftet 
interior,  q^ua.ntum  prcipct  cjjtcripi^.  DX^^s  :  $i  li^ 
gnuifi.  dicitur  ^e  pQrjQTup?  id^o.,  qui^.aeran^  tra]?/mit«i 
tit:  oppi^t^  yitrupx  f^iy  c^Te  ^Oji^okim,^  quia  noUus  per 
i^jramr  aer  (cnfibilji^s^permeat.  ^,  P^  (^quc>..  ^.  ne^ 
qiie  fl^ida.m^  aliud  c  c-  lux^  ctjlor  &c*.  yiti;um.  per«;iear^ 
C»  C.  ii  p^rmcat  N;;  C;  Cur  fiuidum.  aliud;  pra^  ali<^ 
iplidab  qaatpiani  pervadat,  in  cauia^  efl;  varia  ^i^orum  ,. 

I  4k  p«r4cu^.»ra.Q\  qiiy!;^mafpm  cajascHP^;ip  cprporis  baa» 


Lex  viriums  5J 

Intudo.  5tio  t  Etiam  divcrfi  corporum  gwiftis  Q)ect- , 
fica  cvincit  poros,  Eft  gravitas  fpecifica  aqu«  a ff  gr»» 
vitatem  aari  ut  i  «d  19.  Ad  mercurii  ot  1  ad  14  &c* 
DtCcrimen  gravitttit  /p^eciiic«  prope  in  (ingQlis  corpo* 
rum  (peeicbus  advcrdtur;  nifi  autcm  plures,  vcl  majoi 
res  fint  port  in  corpore  uno ,  quam  aiio ,  noUii  habebi<* 
ttir  rat^o  adftfucnds  diver&  gravitatis  fpecific^  ;  crgo. 

ScM.  Ad  porofitat^m  matcrix  objicimitar  (e« 
qtenria  :  L  Ex  divcrfa  flaidorum  tranfmiflifone  non 
refte  infertur  corpora  omnia  effe  porofa ;  ergo.  Pr.  A» 
Licet  fiiber  fit  magis  poro&m  Hgno  quercino,  tomen 
litber  tam  facile  exhalationei  non  tranfmittit  ;  orgOa 
1$^.  N.  A.  Adl  Prob.  dico  :  ideo  iftud  evenirc',  quia 
iliber  conftat  partibus  magis  fleidlibus  &  intumefirenti.* 
bus;  hinc  fit,  ut  earum  pori  maiores  facile  •bftruan*^ 
txir^  &  obftrufti  flniduiH  non  rranfmitrant.  At  quercus 
•onftat  partibus  rigidis,  &  firmis,  non  facile  intumefiren* 
(ibns,  ac  proinde  minus  aptis,  ut  per  eas  pori  obftruan« 
tur ;  ergo.  Dtces  :  Si  ex  tranfmiflione  fluidomm  e- 
tincituc  porofitas  corporum  :  corpbra  magis  porofi  fa« 
eiiius  tranfmittet>t  flaidum,  quam  minus  porofii ;  atqui 
iihid  non  fit ,  ut  doccmur  ex  memorato  fiibere  ;  ergOt 
])E.  D.  M.  facilius  rranfmittent  flaidhitn  catefis  pariiuf, 
fd  eft  :  nifi  pori  qnorandam  corpornm-  obftruantur  pei^ 
partes  adniodam'  flexiles,  &  &cile  intumefcentet  C.  MV 
fi  ebitraafntup  N.M.  Stc  O.  m*  &  K.  Cm. 

Hr  Si  cor]ior»  0fiwi#«  fiinr  porofii,  omuta  tranfinit* 
lent  liicemy  proindeque  omui»  erunt  diaphatM  ;  non  au«> 
tem  tranrmittunt  ;  erg».  ^  D.  M«  omnia  corpor» 
fiikem  in  tenuet  lamollas  ca(a  tbinfmirrent  lucem  C> 
M.  non  fie  didufta  N.  M.  G.  m*  &  N.  Cm.  Ut  cor« 
pus  aliquo^  diofhaiHm  fir,  ncque  impediat  vifionem  iA>^ 
)edoram  externorum,  (ed  lucem  ab  iis  rcflexam  tranf- 
mittat  (  hoc  cwjm  voco  A«tff^«yov  )  non  fufficit*  pr*- 
iirameOe  pori^  pef  qaot  UHnen  ptfrMcrc  poflit ; 

'       D  4  ,  opor 


5$  Se^  h  Caputlh 

eporcet  etm  habcri  pororum  difpQiitionefn ,  «t  htmenj^ 
quod  »}ii  linea  rc&A  non  prQp^gauir/  (ervart  poHit  du 
jpe6lioneni  fuaoa.  At^ai  raro  iittud  accidit,  prs^ertim 
^um  corpora  funt  deniior»  ;  crgo  etiain  in  f^rofis  go¥« 
porilui&  rara  ^unt  diofbana. 

4 

lU,  Si  corpora  oinnia  cffQn^  poroft ,  li^uoxes.  noa 
paffent  comincri  in  vafij ,  fed  efllucrenr  pcr  poros'va^ 
lorum  ^j^  falfum  qft  co.nfij<iu.ens  ;  crga  ^  s^rccedens^^ 
^.  D.  M,  ciRucrent ,  (\  povi  vafovum  forent  (atis  aou 
pU,  S^  (ut  fic  dicam)  6gurd5  conveuietiris  /  ut  particula^ 
clemcntares  fluidorum  poros  iUQs  pcru^c^re  p^nt  C^ 
M.  fcciis  N,  M.  C.  ui.  ^  N.  Cm^  Vt  iiquorcs  efQuant 
t^  vaffs ,  non  fuiiicii  habcri  pQros  >  ftd  oportc^  vaforurai 
f>oros  effe  fitis  amplos^  ac  figurs  c(>nveuienti&  ratuimit 
iiuidoram  moteculi»,  -  Ssepc  vero  pori  corporum  zu 
£liores  (imt,  &  alterius  figurs  ^  quam  minims  panicula^ 
fluidorum  ;  unde  tum  li^uores  non  cfSuunt  per  poro^ 
vafolrum,^  nifi  adliibica  vi,  <]uj;  pores  diflendat^  &  am<« 
pHor^s  effieiat.  Sic  e.  c  fi  va$  mctallinum  implcatujf* 
fiqua„  &  exadiffimc  claudim  fortitcr  comprimatur  ; 
«qua  eontenta  in  vafe  per  poro^  metaUi  egreditur^ 
c|usqi1e  parictibus  cxtrin&cis»  adh2ere.t  in  forma  roriSj 

IV.  Saltein  nonnijlte  tcnuiores  particulae  evapora* 
rcnt  per  poros  cujuslibet  vaiis  »  atqui  nc  iftud  quidem 
fieri  advcrtimus  ;  ergo.  Pr.  m.  in  tubo  vitreo  hcrmeti«» 
ce  ciaufe  fcrvantur  iiquQ:rcs  plurium  annor^im  intervak 
lo  (inofeniibili  dimimitionc.  11.  Si  intra  campanam  vi« 
tream  di&o  antli»  fbrtiter  adhsrentem  repofita  iint 
corpora  muitum  oientia ,  alias  vividtflimam  £cii(ationetn 
oxeitaro  aptlHima,  non  tamen  odor  uUus  percipitur,  hq 
ab  iis  quidem,  qui  delieatiflimo  oi&fia  funt  inftru^i^ 
3^.  N.  (equelam  M.  ratio  eft  :  quia  non  omncs  partk 
culx  «tcunque  oxiles  apt9  funt  ad  fubingrediendum  po« 
yos  qnorumvis  corporum,  qui  penes  diverla  corpera  di« 
^erfimode  configurati  funt;  ergo  neq;  pet  ppres  ^afis  fttju^  ~ 

Vt^t  cvaporarc  ^Swu  Alu  hanc  nupacm  (;g{)%aar um  \ 


V 


Lex  vlrium.  57 

qnU  pjtnleulx  feniiiorcs  adbxrent  toti  maiTtf ;  nec  a1> 
ea  j[eparantur ,  niii  aer  imroediate  ambiens  eas  extellat. 
Sed  in  tubo  Wcreo  aere  eracuato,  tum  hermetice  clan(b 
acr  non  penetrat  poros ;  nequit  et^go  tenuiores  corpo^» 
rum  particulas  tangere,  proindeque  nec  attoUere*  Qna- 
rc  non  poflunt  pafticuls  tenuiores  erumpefe  pcr  porot 
Vi^M  vitrei.  OiTCerum  vitri  porofitatem  abunde  evi£^am' 
babeqiuf  ex  tranfmiflione  lucis  ,  &  parttailarum  ignea^» 
t^um*  ..  Si  aiias  tenuiores  moleculas  non  tranfmittit, 
Iftud  Colum  infcrre  licet  :  froindt  pori  vajoriim  vitreo^ 
rum  noft  ita  funt  difpofiti ,  ut  aiicrum  corporum*  CavQ 
tamen  infcras  s  ergo  vitrum  non  efl  porofum,  , 

V,  Si  corpus  omne  oirec  porofum,  etiam  omne  tC 
ict  intcrruptum  ;  acqui  non  eft  ;  ergo,  Pr.  m,  Nihil 
intcrruptioms  advertitur  in  plerisquc  corporibus,  e,  c. 
s(uro,  ligno,  lapide,  adamante  6(c«  ergo,  I^.  C.  M.  N*m. 
interraptum  cnim  (pcr  Mmpfyf)  dicitur,  inter  cujua 
partes  alias  locum  habcrc  poiTunt ;  atqui  inter  omnium 
corporqmpartcs  ali^ locumfaaberc  pofluntji  ^^go  omnia 
^orpora  fuiit  interrufta^  AdPr.D.  A.  nihilinterruptionis 
fldvcrticur  qcuIo  non  armato^  C.  A,  armato  N.  A.  &  C, 
Sique  armatis  eciam  fcnfibm  inccrrupcio  non  obfervc^ 
tur,  at  ratiQcinio  cr«i  poccft*,  imo  dcbct. 

VK  Adnndis  poris  (equicur  1  nuUnm  corpus  efle 
€ontiuunm^  aut  cafttiguum\  vei  certeinter  continmmy  & 
^ontiguum  &tis  diftingui  non  poftp ;  atqui  dantur  cor« 
pora  tam  continna ,  quam  contigna ,  inter  qus  (emper 
Ui(ccmi  poffit  ;  ergo.  Pr.  M,  Continnuin  eft,  cujus 
partibus  nihil  interCeri  poteft.  Contigua  €\\m ,  quorun^ 
laperiieies  ita  conCbciantur,  ut  (9  (c  tangant,  ip(a  tamcii 
mancant  piuray  nec  unum  quid  efficiant.  Atqui  ii  coi^^ 
pora  omnia  cftent  porsia,  corum  moleculis  aliqutd  intftr-* 
&ri  poftct ;  itemque  eorum  fuperiicies  non  ica  confe. 
ctarcntur)  ut  Cc  (etangant,  &  mutuo  conta£lu  admiflb 
sdhuc  plura  maneant;   ergo  neque  darentur  corporai- 

Vmit^^i  nc^Q^  caf^j»A«      ad9  9  non  modo  corpua 

9 }  w»v 


5$  SfSli$t  Capufir^ 

0jitiguum9tkt  int^rftinf^uai  poris,  fcd  &  epftnnyiHff^  ; 
fto  ituer  c$jitifmumy  &  tomiguum  (atis  di^ccrni  noa  po-d 
^c.       Ify»    D*  M.  {e4}uitur,  nulluin  dari  corpus  coitstU 
ifiiumy  aut  eomigjium  in  fenfu  y?r/^o  ^  6l  Matbematic9  ^ 
^ve  td  eum  rlgorem  loquendo,  qui  Philo(ophum  de^ 
^t  C^  M.  in  ^nfu  huiort^  h.  e.  nuUufn  dtri  eorpu» 
^;;m/«»f»y  aut  eoHtigunm  app^entir  N,M,     Sic  £>•  m» 
^  N.Cm^     Ad  Pr-  D^  i.niain  parr*  M.  Conmiuum  rigi^ 
de  aeeeptum  e&^  cujus  partil^us  nihil  i»tqr(eri  poceft  C* 
|)»^  p;irt.  viiuus  ri^gide  JjumptJim    Sfiidifi.    cujus  ptrtibu» 
pihU  ituerl^ri  fQtcQi^eem  ad  fenfnm  vuigi  C.  euju» 
partibus  otnim^^  nHfii  in,ter{eri  poteA  N.  imam  par.  M. 
P.  etiam  ^dani  CoHtigna  funt,   qnorum   fuperHcies  itz 
^onfbciantqr,  vrt  (c  fe  tangant  adfenfum^  &  apparenter 
C,^  b.  part.   yere,  ac   Marhematice  N.   jdam  part.  M. 
$tc  D.  m.  &  N.  Cm.     Continuiim^  &  contigunm  \n  fenfli 
^gido  acccptum  jam   alias    a  rerum  natui^a  exclufi  itf 
fiietapB,     A^"iWis  tamcn  poris  ajo  dari  corpora  conti-. 
nuay  &  cojirigua  fenfu  niinus  flri^o  acccpta,  intcr  quter 
^fficienter  di^^erni  pofllt  ;    dantur  enim  compofita  , 
quoruui' ptrtes  (ic  miituo  coha?rent ,   ut  iimm  quid  effi-. 
>c\^x\X  faltem  judicio  fenfnnm  \    &  hsec  voco  continua  mi» 
n»i  firi^^  accepta.     Dantur  item  moleculae,  vcl  corpora, 
quac  Ofifenfnm  (c  contingrunt  (^cundum  fuperficiem,  itar 
ttmen,  ut  ttnym  extenfiim  non  efficiant ,  fed  etiam  fett" 
jfiwn  judieie.  mancant;  plura ;    $t  hatc  appello  contigum 
\f\dcm  minps  firide  (ujinpta, 

VII.  Si  eorpora.e(rent  poro&,  propter  innumcrabi- 
Us  hittus  (uo&  £icile  (ut  in  elementa  diOblvercntur ;  at« 
qui  nou  diirolvantur ;  crgo<  Pr«  M.  Quia  in  cumulo 
c.  e*  farime,  trenularum  &c.  habentur  copioH  hiatus,  fa- 
cil#  id  gcnus  acerW  di(rolvun,tur  ;  crgo  a  pari.  ^^.  D. 
M-  facilc  in  fii»  elementa  difToIverentur ,  nifi  periculo 
Jbtiiic  ctiitum  eiroc  per  noftram  de  cohxfione  {ententiam^  , 
flutm  paulo  inferius  referam  C.  M.  fi  cautum  eflN.M. 
V*.f9*  &  N*  Cm.      Cumultts  arcnultmm  unum  eft  per 


^regt^tiffnem  y  in,  q»o.  arennla  non  !ti  eoii.ib<H«iar  altc-» 
ri,  ut  fiufuum  jtidicio  ununi  qukl  cfficiat  pcr  cohxiio* 
liem  debico.  (enfu  intelle£latn.  Contrarium  ha^ctur  isi 
iingulis  corporibas  poroiis ,  quorum  moleculs  ita  fibi 
•on&ciantttf .  ut  admiSis  hiacibus  bene  m.ultir  adbuc 
VH^.  ^H  emcian(;er  vernm  CQbafipnpn^* 

Vlllt  Qu«  porofifunt,  comprimi  poflimti  atqui 
^%ion  omnia  corpora  comprimi  p.offunt ;  ergo  ncc  omnia: 
pofoia  fiint.  Mt  ccrta  cffe  videtur ,  nani  ?x  comprefii- 
Oiiitat^  corpo^u.m.  inf5?rtur  corundcfjn,  p<y;ofitas.  Pir.  m* 
Aqna  null»  a^ttt  comprimt  poteft,  nt  habet  Clv  Ma« 
ichenbtock ,  Acadi^mict  Fl.orentini.  &c.  y  crgo*  ]^« 
D».  M,  comprimi  poffunt,  (i  apta  comprcfiont  inftra^ 
inenta  babeantui^C.  M*  (ecusN.M.  iic  I>.  m.  {ScN.  Cm. 
Puto  cgo  \  corpof^  omnia  hucufque  cognita,  de  fe  ^  Sc 
^fohite  (iin^  oQLmprcflilia,  licct  ndii  a(tu  camprimanttir^ 
^  iicet  cotQiTi  cqmprimen4otum  modus  nos  ad  btme 
'  ii(que  diem.  hteat.  (^Mir^  iterum  ccnfeb :  cx  comprci!^' 
fibiJiiate  q^idifm  rcfib^  inferri  corporum.  porofltatcm  ^ 
|ipn  tamen  negat^  campre{fibi.litate  rsjptBiva^^  (  qus  vt« 
ribusi  ha^^us  <?Qgnj^s  ficri  po6it  )  i?e£lc  ncgari  poro*  ' 
fitatem  corporum,  e»  c.  aquat ;  tum  quod  alfoiute  com^ 
priinr  poflit  corpqs  i^iquDd,  licet  hodie  coroprimi  nc* 
qs^cat  i   tiim  quod  porofitas  ex  aiiia  |»h«npm.onis  GxfB,^ 

IX^  Coi^primitur;  a^ri  in  iclopc^  pneumattca ,  9^ 
hinc  pprofus  j^d,i(;^tur; ;.  cjngo ,  cum  ^^  tdyer&  egqam 
^qrop.rimi  non,  pofliti  p.orQft.,non.  clfc,  ^a;.  D*  0.  fl 
^equ^e  luccm-tra[n(inittiti  nequc  corporoiatia  in  (e  rcci*. 
'  pic  nou  aitHo,  volun^iHe,  neqMe.ullt,«|li%  porD(itatt&  pkau 
ngipena  proditC^C.  fecosN.  C».  Aqua  jam  coniprelL 
^effe  ccnletur ;  q^uid.4gitut^  roiram ,  ii  deinciqis.  com^ 
pr;roi  nqn  poflit  9  Ae^  btft  iloQer  jam  oompreflii&  dafi., 
ficulter  comprimitar  i^ltra  ^  valnminis  fiii-;  qoidmi.. 
IW^^&  iq(i«i,,%^fl^Qrcitis.Q£ungc&tkilplasfm|C^^ 

bct 


€0  ScSioK  Caputlf. 

bct  fiih  eodcm  voluniinc ,  oh  rigorcin ,  flc  denfitttetn 
fiiam,  adeoijue  majorcm  rciiftentiam  fenfibiiiter  eomprU 
mi  ncqueat? 

I 

X*  Dignofci  non  poteft  qnantitas  pororum  ;  erga 
fieque  ccrtum  quid  habcri  potcit  dc  porofitare  corporum.: 
Pr#  C.  Si  ecrta  habcrctur  poro{ifa$  corporum ,  eiiam  di.  | 

gno(ci  poflTct  quantitas  porofcum  ;   atqui  non  poteCl ; 
«fgo^      ^*  D»A«  dignofci  non  poteft  quantitas  ai^/if^^      j 
u  pQror^in,  Gvc  detcrminari  non  pdtcft,  qoot,  &  jquan-» 
ti  in  corpore  aliquQ  habeantqr  porv  C.  A.  quantitas  re«  ^ 

Jativa  pororumK  fi  corpus  unum  confcratur  cum  altcro  J 
N.  At  Sk  C«  Oetcrminatov  gravitof  fiecifita  corpornm  ^ 
divcrG)rum ;  crgo  &  quantitas  refpe^iva  pororum,  (ine  \ 

^ua  diverfa  gravitoi  ffecifica  intcIUgi  non  poteit^  Ccrte 
Corpus  ffecifice  levius  magis  porofum  elTc  dcbet  ipccifice 
graviori ,  quia  fub  codcm  volumine  minus^atcris  h»- 
bct,  ac  proindc  plus  babct  intcrilitiorum  vtateria  fro* 
fri^  d^ititutorum,  h,  c,  forarunt^ 

XI*  Si  corpora  omnia  fnnt  porofi,  tranfpiram  om^ 
nia;  fallit  in  omuiiui  tranfpiratio ;  crgo  &  poroflras» 
Pr«  m«  !•  ii  omnia  tranipirarcnr,  (ive  cfflovia  quspiam 
cmittcrcnt ,  minucrcntur  pondcrc  fuo.  II.  vigore  fuo 
dciUcuerentur.  lil.  Sublndc  prorius  cflc  dcfincrcnr. 
Atqui  nibil  iilorum  advertimus ;  iic  aurum,  vitrum ,  la^ 
ipldes  &c.  non  attritaf  (ed  probe  cuftodita  nibil  de  pon- 
dere  iuo  amiiiiTe  dcprchenduntur  ;  neque  vigorc  fuo  de« 
iHtuuntur ;  mrnus  cfle  dciinunt ;  crgo.  IV.  in  rcgio* 
nibns  oalidis  abundaret  vencnum  o  plantis,  herbis,  ani- 
malibus  &c«  copio(c  tranlpirans.  j^.  C..M*  N.  m.  ad 
Fr.*I.  D.M*  minucrctur  pondere  £lio  inJeHfihiiiter  (qm^ 
iciiicet  non  omnia  tranipirant  finfiiiliter  )  C.  M.  mi* 
nuerentur  fiftfibiliter  N.  M.  C.  m,  &  N.  C,  Grahumi 
itmbra,  vel  raofci  iiccc  continuo  odorcm  Ipargat,  tamen 
poft  annos  aliqnoc  cjusdcm  cfl:  pon^eris,  cnjus  ante  ah«  | 

nos  conipiarcs.      Ratio  tfi  incrcdibilis  fubtilitas  efflu-  \ 

fioiuiPi  quoroin  piurcs  miUionct  ia  minima  fenlibili 

p$pti' 


partkuk  continentur^  quod  dicam  ad  ttiatetiain  de  0- 
'vifibilUaie  corporum.  Quamdiu  igitur  tranfpirare  pote- 
tit  (cniibilis  una  naolecula  ?  sfdo  .*  quia  ja^tura  mole* 
culariim  tianfpirantium  compeufari  poteA  per  particu* 
las  hcterogeneas  fubin  occurrentes,  inque  poros  Ce  iniir 
nuantes.  Fieri  certo  poceit,  ut>  quantum  cfHurioruna 
dilabitur,  tantum  aliens  materiae  accedat.  Sic  coropen* 
^labuntur  omnia.  Ad  II.  &  III.  eadem  eft  refponfia. 
Ad  IV.  J^.  D.  A.  abundaret  venenoiti,  {imulque  abun- 
darent  efRuvia  falutaria ,  Sk  fic  jufta  Kaberetnr  attempe- 
ratio  C.  A*  no^  abundar^nt  efHuvia  falubria  N.  A.  & 
Cm.    ^ 

CoroU.  K  Si  ncquc  corpora,  neque  entia  fimplicia 
{e  mutuo  contingerc  queunt,  debet  intcr  ca  intercedere 
fpatium  (Videlicet  imaginarium)  omni  torpgre  phjfice  txi* 
Jjente  d^flitutum^  quod  vacuum ,  &  iuane  flri^e  tah  di- 
eimus.  Spatiolumy  quod  inter  corpora  ad  fenftim  fc 
contingentia ,  aut  inter  molcculas  minimas,  vel  punflt 
cjementaria  intercedere  debet ,  plane  exigtmm  efl  ,  a« 
{)rope  imperceptibllCj  vel  certe  incapax  recipiendi  alicu- 
jus  fiuidi,  quod  vacuum  dilJemiaatnm  nominamus.  De* 
bet  ergo  in  naturd  admitti  vacuum  dijfemijiatum  ftriSt 
taU. 

Anuotatt^ :  Nbn  hic  contendo  (^ri  vacuutn  coacer^ 
vatum,  {ivc  Jpatium  myuf,  &  notabile  omni  corpotc  C4- 
rcns,  quod  num  detur,  in  Al^ronomia  phyfica  fubinde 
cxaminabo.  Nequc  attingo  vacuum ,  ut  nonnuUi  vo* 
cant,  feparatum,  quod  inde  a  fuperna  mundi  fuperficie 
in  diflantiam  infinitam  cxtcnditur  ^  de  ouo  kiemini  du* 
bio  e(Te  licer.  Minus  ago  de  vacuis  ^Uano ,  &  Tor' 
ricettiano,  ab  authorc  fuo  iic  ditVi) ,  quorum  prius  dici- 
tor  ipatiom  deflitutum  aere  denfiore,  &  crafBore,  quan* 
do  is  ope  antliiT  ita  exhanritur,  Ut  rarifnmus,  fentieque 
noUius  cfFcftus  capax  cvadat  j  poflerius  vocamus,  quotl 
babctnr  iu  fuperiori  parte  Baroipetjti  ^  utrum^ile  eft  v^* 

Cttum ' 


-^ 


€q  ScHioK  CaputlL 

bet  fuh  eodem  voluroinc ,  ob  rigorem  ,  &  detilittttem 
iuam,  adeoquc  majorcm  refiftcntiam  fenfibiliter  eompru 
mi  nequeat? 

1 

X«  Dignofci  non  potcfl:  quantitas  pororum  ;  crgo^ 
nequc  ccrtum  quid  habcri  potcit  de  porofitatc  corporum-. 
Pr»  C.  Si  ccrta  habcrctur  porofiras  corporum ,  ctiam  di. 
gnotci  pnffct  quantitas  porotum  ;    atqui    non  potcft ; 
<rgo«       55-  ^»  A,  dignofci  non  poteft  quantitas  abfolu^^ 
ta  poror^m,  fivc  determinari  non  pbtcft,  quot,  &  quan-» 
ti  in  corporc  aliquo  habcantqr  pori  C.  A.  quantitas  re- 
Jativa  pororiim]^  fi  corpus  unum  conferatur  cum  aitcra 
N.  Ae  &;C,     Dwvminn^x  gravim  fpecifita  corporum 
iliverfbrum ;  ergo  &  quantitas  refpe^iva  pororum,  fino 
qua  diverfa  gravim  fpecifica  intcHigi  non  poteft*     Ccrte 
COrpus  fpecifice  levius  magis  parofum  cftc  dcbct  fpccifico 
graviori,  quia  (ub  codeni  volumine  mlnus  inatcris  ha- 
bet,  ac  proindc  plus  habet  intcrftitioxum  viateri^  pro- 
fri(^  d^ftitutprum,  h,  c,  porarunh 

XL  Si  corpora  omnia  funt  porofii,  tranfpiram  om, 
nia  ;  fallit  iti  omnibui  tranfpiratio  ;  ergo  &  porofitas. 
Pr.  mt  !•  fi  omnia  tran(pirarent ,  fivc  cffluvia  qusepiatn 
cmittcrcnt ,  minuerentur  pondcre  fuo,  II.  vigorc  fuo 
deltlruetentur.  lil.  Subindc  prorfiis  c(k  dcfinerenr. 
Atqui  mbiliftorum  advettimus;  fic  aurum,  vitrum  ,  ]u 
yidcs  &c.  non  attrita,  Ccd  probc  cuftodita  nihil  de  pon^ 
dere  fiio  amififie  dcprchcnduntur  ;  ncque  vigorc  fto  dc* 
iiituuntur;  mmus  cfte  dcfinunt ;  crgo.  IV.  in  rcgia« 
nibns  oalidis  abundaret  vencnum  c  plantis ,  hcrbis ,  ani- 
malibus  &c.  copio(c  tranfpirans.  iji.  C.  M.  N.  m.  ad 
Pr,-  L  D,  M.  minucretur  pohdcre  fuo  itifenfibiliter  (quiii 
icilicct  non  omnia  tranCJMrant  fenfibiliter  )  C.  M.  mi. 
nucrentur  fenfibiliter  N.  M.  C.  m,  &  N.  C.  Granuin 
cnibra^  vcl  mofci  licct  continuo  odorem  Qiargat ,  tamea 
poft  annos  aliquot  ejusdcm  cft  pondcris,  cujus  ante  an- 
nos  complures.       Ratio  efi  incrcdibilis  fubtilitas  cfflu- 

vioruin  i  quorum  plurcs  milliones  iii  minima  fcnfibili 


pArticuk  continentur,^  quod  dicam  ad  matetiflm  de  di- 
'vifibilitate  corporum,  Q^^*'^^*^^  igi^ur  tranlpirarc  potc- 
tit  rcniibilis  una  roolecula  ?  .  sdo  .*  quia  jadlura  molc* 
cuknim  tranfpirantium  compcnfari  poteft  per  particu- 
las  heterogencas  fnbin  occurrentcs,  inquc  poros  fe  infir 
nuantcs.  Fieri  ccrto  potert,  ut,  quantum  cffluviorunx 
dilabitur,  tantum  aliens  matpris  acccdat.  Sic  Compcn* 
^labuntur  omnia.  Ad  II.  &  III.  cadcm  e(l  rcfponiia. 
Ad  IV.  ,15^.  D.  A.  abundarct  vcncnom,  fimulque  abun- 
darcnt  cffluvia  falutaria ,  &  fic  jufta  h^abcrctnr  attempe* 
ratio  C.  A.  non  abundiirent  effluvia  {alubria  N.  A.  Qc 
Cm.    ' 

CoroU*  V.  Si  nequc  corpora,  neque  cntia  fimplicia 
(c  mutuo  contingcrc  qneunt,  dcbet  intcr  ca  intercedcre 
fpatium  (videlicct  imaginariimi)  oinni  corpgre  p/jyfice  exi- 
J?eM^e  djeflitutum,  quod  vacrmm,  6c  ina^ic  /iri^e  tale  di- 
Cimus.  SpaTiobon^  quod  inter  corpora  ad  rcnflim  fe 
contingencia ,  aut  inter  molcculas  minimas,  vel  pun£la 
clemcntaria  intercedcrc  dcbet  ,  plane  exiguum  efl  ,  ae 
propc  imperceptibilc,  vcl  ccrtc  incapax  recipicndi  alicu- 
jus  fiuidi,  quod  vacuujn  di[leminatmn  noininamus.  De* 
het  ergo  in  naturd  adviitti  vacuum  dijfcmiuatum  firi^t 
,  lale. 

^nnotatia :  Non  hic  contendo  d^ri  tacuufn  coacer*^ 
vatum,  (ivQjpatium  inajuSj  &  notabile  omni  corporc  c^- 
rcns,  quod  numdetur,  in  Allronomia  phyfica  fubinde 
cxaminabo.  Ncquc  attingo  vacuinn ,  ut  nonnuUi  \q* 
cant,  feparatujn^  quod  indc  a  uiperna  mundi  fuperficie 
in  diflantiam  infinitam  cxtcnditur,  de  quo  jncmini  du- 
bio  eflc  iiccr.  Minus  ago  de  vacuis  B^leano ,  &  Tor- 
riceUiano,  ab  authorc  fuo  (ic  dicViS ,  quorum  prius  dici- 
tur  (patium  deftitutum  aerc  denfiore,  <Sc  crafliore,  quan. 
do  is  opc  antli*  ita  cxhauritur,  ut  rarifrimas,  fermcque 
nullius  cffcftus  capax  evadAt  \  pofterius  vocamws,  quod 

habctur  iu  fupcriori  partc  Baromctri  3  utrumcjuc  eft  va,- 

cuuin 


o 


(S2  ScSIioL  Caputlf. 

cuum  minus  fttiftc  talc.  Vacuum  vulgare,  &  ruflh 
iufjty  qualehabctur  indolio,  vel  marfupio,  in  quo  npti 
reperiuntur  ea,  quibu$con(ervandisdc(iinarum  eft,nun* 
quam  nominabo.  Contra  (blos  Cartejtanos,  &  Peripate^ 
ticos  ago.  '  Cartejius .  qvLidem  cum  fuis  vacui  pojjibilita* 
tetn  negdt ,  fteque  tamen  ejus  impojjiiilitatem  probare 
potcft;  quid  cnim  repugnantis  invoivac  idca  e.  c.  Aulx 
Academicx ,  in  qua  nullum  omnino  corpus  habeatur  t 
an  fortc,  quod  haberctur  idea  intervalli  cu)u(piam ,  {ive 
^xtehfiy  iine  idea  (blidi  ?  Atqui  vcro  habcri  poteft,  cumi 
rxfef/^i)  concipi  poCCit  Jme  cognita  corporum  rejfijlentia  ^ 
quam  tamen  involvit  foliditas,  Peripatetici  etiam  va- 
cuum  inficiabantur ,  naturamque  ajebanc  adco  a  vacuo 
omni  abhorrcrc,  iit,  ii  corpora  inter  duos  muros  mcdi« 
annihiiaredrur,  continuo  muri  ad{e(e  invicem  acccde- 
f  c,  procurrere,  &  provolare  debcrent,  aias  Aippcdicante 
fraclaro  ilJo  horrore  vacui,  l^trorumque  rationes  bre* 
vicuie  proponam ,  6c  diflblvam. 

/ 

ScboL  pppon.  I.  Vacuum  dicitur  Q)atium,  (eu  in« 
tervallum  omni  corpore  deftitutum ;  Ccd  cale  ihterval* 
lum  implicat;  ^^^g^*  Pr.  m.  Intervallum  hoc  eflct  va* 
puum ,  &'  non  cflct  vacuum  ;  crgo.  Pr.  A.  cflct  va» 
cuum,  ut  fupponitur  ;  &  non  eflet  vacuum ,  quia  eflec 
cxtenflim ;  extcnfum  autcm  omnc  «ft  corpus  >  crgo.. 
Ify.  C.  M.  N.  m.  ad  Pv,  N.  A.  ad  hujus  Pr.  C.  imam 
part*  A.  N.  adam.  Caufiilcm  D.  quia  cflet  cxtcnnim 
iifiaginarinm  y  &  mere  pojjtlile  C".  aflualc,  &  phyfice 
exiftcnsN.  Extenjttm  reale,  ac  pJ^Jicum  (pcrOncol.) 
dicimus ,  quod  conftat  partibus  extra  fe  fe  pojttis  fnltem 
judicio  fenfuunt  conjuiUlis  ;  atqui  vacuum  non  conftat 
jejufmodi  partibus  ;  crgo  non  cft  extcnfum  phyficum. 
Ke£le  tamen  dixcris  eflc  extenjiim  poffibile ,  quia  in  co 
locari  pofliint  corpora  conftanria  partibus  cxtra  fe  fe 
pofitis.  Alii  fic  refpondcnt :  vacnum  cflet  cxtenflim 
rarione  iimirum  C.  A.  rarione  ftii  fubd*  pcnetrabiiit^ 
C.  A.  impenctrabiiitcr  N.  A«  &  Cm. 

II: 


c 

Ltxviriwr.  €j 

It.  Si  t>£as  thnihtUret  omnia  corport »  qnft  t.  c, 
\n  concbvi  aliquo  contiiieiirur,parittet  conclavis  (o  tan- 
gere  deberent ;  ergo  hoc  ipfo  non  dtrecur  vacuum  ,  ac 
proinde  nunqnam.  Pr.  A.  illt  (e  tangnnt,  inter  quit 
Dihii  intercedit ;  atqoi ;  ergo.  l|t«  N.  At  ad  Protit 
D.  M.  inale  tangunt^  tnter  qus  nihtl  iittercedit,  ncc 
intercedcre  poteit  C  M.  fi  quid  intcreflc  poilit  N.  M. 
^iic  D.  m.  &  N.  C  nihil  quidein  tdu  interponeretur  in* 
ter  parietes  illor»  (cd  ttmen  intcrponi  poflet  ;  ttqae 
tfiud  (iifSeir,  nt  pariete^  (t  tangerc  dictntur. 

III.  In  fa£Va  hypothefi  foret  diftantit  intcr  parietcD 
erge  aliquid  elfet  inter  illos  parietcs  ;  tc  proind:  nou 
litbcrctur  vacuum.  I^.  D.  A.  fbret  diitancia  inter 
parictcs  hoc  fenfu ,  quod  aliquid  iis  inrerponi  poflec 
C.  A.  quafl  a^u  interponerctur  aliquid,  unde  corum  di* 
ftantia  rcpetatur  N.  A.  &  Cm.  Diitanrit  in  (e  fpcdttt^ 
flc  ratione  flii  non  eft  ens  afiqucd  fbyficum^  (ed  mere  r$* 
ffeBivtim  ;  didarc  enim  dicunrur,.  intcr  quot  tcrtiuni 
quoddam  cxtcndim  vel  rc  ipfa  intcrpouitur,  vel  ixs  iiiv 
ihotis  interponi  poteft.  Qutrc  Itcet  in  hypothcfl  tnni- 
bijiatorum  corporum  retiquorum  inter  geminos  parictcji 
nihil  inrcrjaccar^  quia  tamen  interjtccrc  potcft^  babtbitiur 
vera  diflanti^, 

IV.  In  ctftt  tUtto  menfartri  poflcr  difttntia  ptrio- 
fis  unius  ab  tlttro  ;  crgo  habererur  aliqnid  rctle  inrcr* 
pofltum. '  9*  D.  A»  poflet  menfurari  diftanrit  rttio- 
M  corporis  interponibilit  C.  A.  interpofiti  N.  A.  dc 
Cm. 

V.  Intcr  ptrietes  illos  eflct  (pttium  omni  corpore 
lieftitutum ;  ttqui  implictt  fpatium  omni  corporc  defti- 
tntum  ;  crgo.  Pr.  m.  (patium  eft  ordo  flmultanco* 
Mtn,exfrt  ftpofitorum,  extenfiontin  ftcientium,  tc 
proindo  tcrto  modo  coexiftentium ;  cr^o  ubi  nullufft 
«arpos  htbotury  implictt  fparium.  ^tdo  i  fpt* 
tium  (  ftr  Mie$afk,  )  non  diflinguituc  t  rebuf  fknulta* 
fftii  cotxifli:iitimt  tof^usm  rn  > «  r$lnis ,  ftd  ttnqutti^ 

mo* 


^4  StBo  J.  Caput  II. 

tnoduS)  five  ori»  nrum  a  rchus  ;  atqoi  iitipHcat  lidberE 
ordinem  reruni)  ubi  res  nullx  (unt ;  ergo*  J^.-D,  M*. 
cflct  fpatium  omui  corpore  aQuali  deftitutnm  C.  M* 
ctiam  f$ffibili  N.  M.  D«  m.  implicot  ^tium  omni  cor* 
pore  tam  aftualsy  quam  pojphili  deflitutum  C;  m»  duii^ 
uxat  a^ali  corpore  deilitutum  N.  m.  &  C.  Spatiunr 
reaie,  (ive  aduale  concipitur^  cum  repra^fentatar  ordo  ^ 
quo  cntM  reapfe  exiftentia  coexiftunt..  Spatium  mer 
fojjiiile  ( quod  alii  vocant  (patium  imagiturium  )  intcl* 
Itgitur)  dum  reprzfentatur  ordo  merc  poffiiilUi  qU9  cn» 
tta  itidem  mere  pojjibilia  cxtra  fe  fc  poni,  iibique  coexi- 
ftere  poffnnt*  Inter  parlctcs  illos  intcrjacerct  fpatiuoi 
non  aftuale^  &  reale  y  fed  imaginarium  ,  &  mere  pofli» 
bile.  •  Jam  coutinuo  liquct  ^  quid  ad  Prob*  (\t  rei^on» 
dendum» 

VI.  Spatiom  intct  geminbs  iftos  parictcs  intcree» 
ptum  eflet  exrenfum  ;  atqui  repugnat  extenfum  omnt 
,  corpore  deftitutum  ; ,  crgo.  i^.  D.  M.  efTet  exceil« 
ium,  h.  e.  argueret  e^tenjibuem  poJJiLikm  C.  M.  realem^ 
live  aBuakm  N.  M^  D.  m.  repugnat  extenfnm  a^ualt 
omni  corpoTC  dertitutum  C.  m.  cxtenfum  poflibile  N4 
m.  &  Cm.  \  Sp^tium  iilud  no»  efTet  a8u  exteiifum^  quia 
non  cfTet  fpatium  a£tuale,  fed  pure  pojjitile.-  Dicef  :  {| 
aoii  efl:  aftu  exteftjiim^  nou  cft  (patium.  ][$.  N.  fequ. 
notio  fpatii  gencratim  fumpti  ston  involvit  exccnfionefil 
femper  a£luaiem  ;  fiifficit  poflibtlis.  Sic  fit  in  cafii  iro* 
ftro;  coiicipimus  fpatium  inter  illos  parictrS)  quia  con* 
cipimus  pofTc  inter  illos  faaberi  exteiiiiotiem  ;  non  verO 
.concipimus  extenfioncm  aliquani  realcip^  aut  corport 
cxtenfa  realiter  a^u  intcrpoiica» 

VlTk    Spatium  geminis  parietibus  interjc^um  aiS 

gtieret  extenfuniim  realem  ^   fcu  aSualem  \    atqui  repo» 

gnat ,  ut  fpa^um  $mni  corpore  dejiitutum  arguat  cxten* 

,    (ioncm  a&ualem  ',  €rg<».      Pr^  M.    fpatium  illud  pofTat 

4ividi  >  ergo.        jy.  N«  M«  ad  Pr.  D»  A*  (OfTct  divi4i 

divi* 


virium»  ^S 

iKvifidiie  imtfinufia ,   &  rcfpondcnte  ^tio  knagmaH$ 
CtA»  divifv)ne  aQmli^  &  rtalit^rh.  &  C. 

VIII.  Admiflb  vacao  lurilns  fieri^poiret  mottis  ; 
ergo  cam  (cmpcr  liaberi  podit  tnotos,  nnnqtiam  iiaberx 
poteft  vecoum.  Pr.  M.  Motus  cft  translatio  riiccciriva 
de  loco  in  locum  ;  atqiii  admiflb  vacoo  non  haberetoc 
diverfitts  locorum  ;  ergo  ncqac  mutatio  locoriim ,  i*  c* 
^cranslatio  lucccfliva  de  loco  in  locum  ;  proinde  nee 
motus.  T^.  N.  A,  ad  Pr.  D.  M.  motus  eft  translatio 
focccfliva  de  loco  in  locum  vcl  aSuakmy  rtXnure  foffim 
Ulem  C.  M.  4^itaxaa  a^uaUm  N.  M,  Sic  D.  m.  Qc 
N.  ۥ  Licet  in  vacoo  non  (it  locus  aBualis^  Ocpkxfi^t 
eft  tameh  paffiblliSy  fivip,  ut  nonnuliis  placcr^  Matle^a^ 
$icm.  Non  eft  loCus  a&uaUs^  quia  non  haberctnrrelatio 
ad  coi:ptts  aBm  exiftens;  eft  poffibilis,  qOia  haberetar  re« 
ktio  ad  corpus  y  (i  qaod  in  eo  iocaretnr.  Atque  locos 
mert  paffiMie  (ufficit  ad  motum ;.  fieri  enim  non  pottft» 
«t  corpoi  focccflive  reipondeat  divcrfis  iocts  affignabili» 
hm^  b.  e.  p^bilibus^  quin  coneipiatur  in  mota* 

IX,  Non  datur  vacuom  caaeervatnm  \  proindc  nee 
iiffemiuaium.  .^.  De  vacao  qutdcm  coacervato  aliao 
me  {criptarom  pron^ifi.  Sit  intcrea  rc^ponfio  (cqucns  s 
D.  A«  non  datar  vacuom  coaccrvatum  in  atmoCph^mi 
noftra  T.  A^  in  celo  planetario  N.  A.'&  Cm«  Scd  nCf 
qoe  de  (yflcmate  planetario  ^  bodie  qutdpiam  definio* 
i^ices  :  in  atmorphaera  noftra  non  datur  vacuum  toaietr^ 
varum ;  nec  igitur  dijfeminamm.  ^.  T.  A.  N.  Cnu 
Di(par.  ell  I.  Vaata  fieitabiliay  &  mqjera  (  qua?  dicimnt 
vacua  tQOurvata )  fadle  replcrx  poflbnt  matefia  aiiqo4 
interiabentCi  admodam  fubtili ,  cuios  exiftcntiam  ncmo 
prudens  in  dubium  vocaverit.  C|:  rcplcri  poflont  ita,  oC 
ashmffa  vama  diJH^uifuuo  necefle  Jion  Gt  poros  ilUus  ma» 
teric  fabtilis  cxpleri  per  aiiud  fiuidum  fubtilius  y  &  fio 
in  infinitom.  At  negato  vacuo  dtjjeminato  opnrrdbit  po* 
fos  corporom  (quos  t/i  omnibus  omnino  corporibus  ^tti 
,    iof  ro  ori^hMi  eft  )  CKpieri  _pcr  matei iam  aii<jaam  intec» 

Ji  >       labctt* 

r 


€6  StSmh  Caputn. 

fobcnteni,  flaidam,  &  CvbtilU^mam ,  iftioiqiie  pim$f:  itts» 
rum  fet  tlitni ,  &  fic  dt inceps  in  infinitaoi,  Dices  t 
emnes  minatidimi  pori  folidi  cujuscunque  expleri  po(^ 
funt  per  fluidam  atiqaod  inrerUbens,  poriqoe  flnidi  iU 
litts  interlabentis  expleri  poflTunt  Jme  procejfu  in  infiuitum 
per  partes  fluidi  alteriusad  motom  aptiflimi,  fluidifllmi, 
oc  recipiendae  omnis  figurflt  capacis.  ^*  D.  ^.  flc  expleri 
foffeui^  fl  non  ipfum  hoc  qualecunque  fluidiim  conflarcc 
poris  T.  A.  fi  conftat  N.  A.  &  Cm.  ii  genus  fluidum  fi- ' 
gmentum  cft  ;  revera  non  datur.  Difpar»  efl  IL  Ke« 
gato  vacuo  coacervato  ncn  (equitur  corporft|  aot  mini« 
mas  corporom  moleculas  (e  fe  inraiediate  contingere» 
Sequitur  negato  vaeu9  dijferhinato^  ut  confi^cr^nti  patct»' 


l^.  ig.  Dcmonftratur  ParsLegis 

Virts  tsupulfiva  fimpir  Junt  mutua.  Pr«  AA\a^ 
ni  contrarta  fenriper  »  &  «qualis  eft  reaAi» 
(  §•  4«  )  9  ^^&^  quantum  corpus  A  repellic 
corpus  B  t  tamum  viciffim  corpus  B  repeliet 
prius  illud  A.    Acqui  fic  vires  rcpulfivas  funt 

^.  19.  Pars  ^tia.  VirtSyiH  mmmis  diftan^ 
fiis  npuJJlvdyfiint  cuivis  Viloeitati  sxftingucnda  pares. 
Vt.  nulium  corpusi  quantacunqut  celeritate  motum^ 
poteft  cum  pracsdente  velocitats^  vel  aliqua  differen^ 
iia  vilocitatis  ad  conta^um  immediatum  perve- 
aiire;  fecus  dabitur  compenetratio,  vel  admiN 
tetur  laltus  in  natura  ($•  17.)  >  ergo  omnis 
yt\oc\tBS,  quantacunqutf  ea  fit,  debet  exftin|rut 
ante  contadum ;  ac  proinde  cum  contaAus 
immediatus  »awra/iirr  nabcri  nequeat  (§*}'^* 
CoroU.  2.  &  30»  debent  vires  rcpulfiv*  cuivis 
:i  exftinguendae  parcs  efie, 


Lex  vfrium»  if 

$.  20.  I^ars  4tt.  Fircs  repulpvd  mminutH 
tn  ififinitum  dijtsntiis  ^refiunt  in  infinitum,  Proby 
Vires  repulfivae  imminutis  Jiftanttis  augeri  dc- 
l)ent;  ergo  imwinutis  in  infinitum  diftantiis  au* 
;eri,  ac  crefcere  debent  in  infinitum.  Pr.  A# 
\  vires  repulfivx  imminutis  dinantiis  non  au- 

gentur,  dici  non  pofTunt  cuivis  veiocitati  ex« 
inguendat  pares;  atqui  pares  elTe  dfbe'nt(^« 
fracesl.)  ;  ^rgo.  Pr.  M.  imminutis  diftantiis 
non  poflet  exttingui  ea  velocitas »  quas  in  ma- 
jore  didantia  exftinAa  fuit ;  nam  in  minore  Ji^ 
fiantiA  ageret  vis  repeilens  minort  tempore  :  in 
majore  d^antis  ageret  eadem  vis  repellens  major$ 
tempore.  Earundem  autem^  vel  xqualium  vi* 
Kium  efFedus  funt  ut  tempora.  Quare  cum  in 
Ininore  diftantia  vis  repellens  agat  minore 
temporei  in  majore  vero  diflantia  majoretem- 
pore;  cumque  vires  omnes  nobis  cognitar, 
quat  aliquo  tempore  agunt  ^  ut   velocitatem 

f)roducant,  agant  in  ratione  temporis,  &  fui 
pGus  (feu  cum  C=:  VT  ,  ut  infra  dicam) 
Soffet,  quin  deberet  vis  repellens  in  major6 
iflamia  piures  gradus  celeritatts  exftingOere, 
quam  in  mtnore;  ac  proinde  vires  repul(iv«e 
in  minimis  diftantiis  non  eflent  cuivis  relocl« 
tati  e};!ftinguend«  pares. 

Prob.  ado.  Si  vis  reputfiva  in  minimis  di- 
fiahttlis  noh  aageturi  poterunt  dno  corpora  ad 
immediatum  contia<9uq|^  pervenire  cum  aliquM 
differemia  veiocitatum,  &  vel  ideo  tompemtrari 

?oterunt;  aut  vero  violabitur  Ux ^eontinuitatis^ 
lihiliftoniai acoidere  pdteft j  ergo«    Pr.NL 


s 


€9  SOh  l  (Uput  IT. 

PrxceisLt  globus  aliquis  celeritire  vs  C;  iftdfn 
Confeqiutur  alius  celeritate  rs  12  ;    debebie 
Vis  repuUiva  ante  contadlum  immediatum  lar 
sUijua  difiantU  exfttnguere  illam  dtfFerentjam 
6.  graduum  velocitatis  ($;i70*     In  alto  ca- 
fu  corpus  fequens  tmpe;llatur  celeritate  t:^  ao» 
corpbre  alio  prccedente  cum  fuis  6.  gradibufi 
velocitatis ;  agec  utique  vis  repulliva  brevi$H  "^ 
Umporiyzc  prius  f  nam  quo  velocitatum.difcri- 
fnen  majus  fuerit»  hoc  major  eft  vehcitaj  refpc^ 
Hiva^  qua  corpora  ad  ^  ^  accedunt»  ac  pro- 
inde  accefTus  celerior  »  tempusque  brevius) 
Vis  igitur  repulfiva  exftingueret  in  aItero.ca« 
f\X  minui^  quam  differentiam  6«  graduum,  cum 
eflFedus  earundem  virium   fint  ut  tempora« 
SuperefTent  igitur  exilinguendi  plures  ^radus» 
jquam  o£lo  (  nam  inter  6.  gradus  corpons  prx^ 
cedentis,  &  2d.  confequentts  intercrant  14.);^ 
hos  nifi  exftinguat  in  minorc  Jifiantia^  poterunc 
corpora  cum  aliqua  cclcritatii  diffcrcntia  pervenire 
ad  contaAum  1  proindeque  compcnctrabuntur ^ 
Vel  violabitur  lcx  continuitatiu 

Scbol.  Prior  lUa  protMtio  (ic  illuftftri  potcft  :  SiC 
In  eorpore  y#'tanta  vii  r^pellcns,  quttnta  in  diftantia 
si  2  cxitingufre  pofllt  diffcrentian)  6»  graduum  velo* 
citatis.  Ponamus  ad  corpof  ^  accedcre  corpus  aliad  S 
cnm  differcntia  i^.  gradumn«  Si  in  diftamia  s  1  cx* 
i^inguatttor  6.  gradus,  fQpcram  adhuc  exdinguendi  9. 
graduS  in  diftantia  :s  i.;  Ifti  vero  exftingui  non  poC 
lent,  (i  vis  repuniva  imminatis  diftantiis  npn  augcretuv  ; 
ergovis  repumva  non  cffct  par  exftinguendff  cuivis  vc- 
locitad  atcunqae  nagns^    Par  au^em  eflc  dcbct ;  orgcy 


'  lixvtrhmH  €9 

'f.  2T.  Pars^ta.  Vis  r$puWv$ auBt  di^anm 
tHs  JtcrefsH^  Mi  in  ipioJdm  JiftmM  admodum  ^* 
gua>  tvAniJiit.  Vu  Vls  repalQva  crcfcit  ttnmU 
fiutis  diftaiitfis ;  ergo  major  efi  in  mimrihus  di^ 
llantits,  minor  in  majoribus ;  h«e.  auffis  diftantiii 
decrefbtt.  sdo.  Vit  repulGva  iftjl^ri  limitisjuost 
neque  ad  quasvis  diftantias  etiam  adhuc  mini» 
fna#  fe  Ct  exporrigit ,  ot  quotidianis  diverfa^ 
rum  cobzfionum  phacnomenis  edocemur  ; 
prrnide  vts  repulliva  in  quadam  diftantia  ad» 
nodum  etigua  itum  ivamfeit. 

g.  22.  Pars  619l.  AuBa  ittrum  diftawtis 
Jhitint  vins  nfulfiua  in  attroBivas  infecntts  pri^ 
iHum  9  mox  dicnjeentis ,  dum  ivanefcant.  Attrssm 
fiio  iterum  ahit  in  repulfionem ,  itirum^ui  rePulJt$ 
in  ssttraBionem  %  & ^pcr  vices  in  pluribus  diftanm 
tiis ,  femper  tamin  adhue  minimis.  Verttatem 
hanc  ex  phxnorrienis  probo :  Omnium  corporum 
snoleculx  minlmx  (h  (e  in  uhimis  difiantiis' rc^ 
pellere  debene,  (ecus  nullum  habebicur  exte»» 
fim.  Repuifioni ,  auAa  paullulum  diftantia 
fiiccedere  debet  attraAio  >  fecus  nuUum  dabi« 
tur  continuum  ad  fet^um^  neque  fibi  particulc 
sninim«  cohatrebunt»  Corpora  dura  fubinde 
di^a&a ,  etjS  glaberrimam  (uperficiem  habe- 
re  videantur,  nulla  tameii  vi  ita  deinceps  fibi 
apprimj  pofltint»  ut  priori  frmitati  cohxreanr, 
^uti  (cillcet  particular  corpus  durum  compo- 
rentes  ab  ea  diftamiaifut)t  remotx,  in  qua  (c 
ie  attrahebai)t  i  Se  delatx  funrad  eas  aiAan« 

tiai|  \u  qmbiu  fe  rrpeUnm;    Repolfie  iUa  at^ 

£  a  ^ifc 


^  SeSUh  CifHtJL 

Aiorem  nexam  impedir»  C^f$r4  m^Uis^  e.  er 
cera»  febum^  argilla&c;  fe  caraprimi  patiua» 
tur  in  plurimis ,  (Sd  Jiverfii  omnino  diimtiis  i  ne* 
(Que  ceffance  vi  cnmprimenre  prtorem  figu^* 
jrim  affum  inr,  fed,  quemadmod^m  compreC^ 
fx  funt ,  Gc  con^Hiff(Hfn  aH  lcufum  ;  qaare  i« 
plurimis  diftanciis  babentur  li^nires,  ^uihui  n 
npulfionc  tr^nfitur  ad  mra^ioncm  ,  in  qutbus  fiw 
}i$  locata  punda  qi^i^fgere  potrunt  ;  frgo  w 
flmimis  iUii  dtfidHtiii  ha4>etur  vtoliicudo  attra* 

dionumt  &  repulfionum^  Corp^ra  psidat  t.  tu 
guttulx^  vel  molecuU  minimap  aquexprimum 
/e  C^  r^pclttmt  m  alfimis  diftantiis  ($•  17«  Cor^ 
st. ) ;  tum  «uaa  paulifper  diftwia  f«  a^rakunji^ 

iibique  cohsren(  ( $^  14.  &^l)%  AUQubi  isi 
minimai  it^rum  diftantia  C^  rcpilb^nt  ^  «beuM 
enim  in  vapores;  iterumquc^  ie  ottrabHnt^qui^ 
Iterum  QOQuot  in  gutt^»  qq«  fubinde  rel»i 
buntur  In  terram.,  Dentqu<^  in  fcKmcnfMioni» 
lus  ^  &  cffcrvifccnUU  obf^irvAnms  particulas  di«^ 
;verfis  vela^itattbus  ire,,  rediret,  lam  ad  f<^  itv^ 
iricem  accedere  i^  jarp  4  fe  mamo  rfcedcre  ^ 
^uam  accefruuni ,  fy,  reqpd^Qixm  «Iternj^tionem 
H  f4M/4  mcjikanicis  reperi  ncyt  nofle,  dicai?!  a^ 
in^teriam  dc  opcrationihus  Ckcmkia.    pebet  er«^ 

go  repeci  a  vKilfititiiiiMi  «ttir«^iofiain  ^  9i  re« 
pulfipaMm^ 


$cbok  l  E»  bfe %pi4m  fhmmtvi^^i&^^^ 

¥1  dmcci^if^ju^  i  «^  rcpuijt^mn^  ahctnatio^  $isx\%  etfiac|( 
{nteUig^i  ppt^»  q\ijei^ad|no4cMn  pro  varicta$e  ^/fasitj^ 
fmm  iim  a^oBio  b^Kttiir,  jsnn  rcpdfio,.    Tria  adhuc. 

^fmmm^  €  M«3^^i«  tfMl^omi  t44«wn^  v^ 


t  1. 

l4X  virium  71 

fcns  doQriiM  fireiens  mlriiice  coniirniablttir.    Poftremi 
^uo  peculiarem  Philo(bphi  •ttencioncni  mcrentar, 

L   Calidt  aqnjc  gtitta  in  Cphmrm  coit  non  mtnat^ 
quam  frigt4a ;  crgo  ejus  moleculde  minimx ,  qnc  m  icl» 

;  _  timu  dtftMtiis  (e  repcJlert  debebant  (  f*  !?•  )>  *o^ 
^uxillum  diftantJa  /e  attrahunr.  Dum  frigefeit,  in  mi* 
nns  rolumcn  contrahitnr ;  e^go  dtnM  nmw^  fmUiJft¥ 
^  diflmM  adhnc  manet  ittr*Ato,  Si  frige(cat  porro, 
ia  ealor  magis,  magisque  diminuatnr,  etiam  abit  in  gU- 
ciem  ;  gCaciata  autcm  aqua  majm  vQlumeii  obtinet,  pro« 

0  indcqut  particnldc  minimtt  magis  ab  imdcem  dtftant; 

[  ied  tamen  {  quod  mirnm  ndebitnr  )  firmii$s  (ibi  cphi^ 

rtnt,  quam  ante;  ergo  au£la  iterum  diibn^tia  itemmhi» 
bctur  attradio.  Hucuique  (  praster  alia,  quc  focile  de» 
duci  poflTnnt  )  minifefte  (equitur  :  iiofi  tiuic^m  datri  dU 
finnttam ,  iu  ^  fonffnlitef  >  agat  sttraifie  ;  fid  fbtrts  ^ 
In  quibus-mofecnlc  minimsr  majorem,  vel  minorem 
cotisiionis  yim  acquirant ;  fic  tamcn|  nt  major,  ant  mi- 
nor  v'\%  cohciioiiis,  vel  ctiam  attra6lionis  non  pcndeat  « 
raticHi  reeifrdca  ditflicata  diftantiarum  minimantm^  ad 
quas  lex  attrftSionis  nullatenus  extendi  poteft ,  nt  tx 
.di£lis  patet.  Parro  s  fi  eadem  guttula  glaciata  igni  ad» 
snoveatur,nonmodo  coliiqne(ctr,Kd  etiam  in  vapores  abit  / 
proditi  ingenii  yi  expanliva ,  qus.  vim  aerts  elafticAiti 
inieomparabiliter  (iiperat,  utvidere  eft  /»  MoUfila^  de 
qua  orercnns.  Htnc  vero,  (equitur :  in  cstigua  quofiam 
diflantia.finfitsadea  bumguos  fitbtetfugiente^  attrgSioni 
fiiccedere  refulfionept. 

IJ.  Laeryma  Ba$avica  (  (ic  dicitor  gutta  vitri  • 
fammo  caiorc  refente  refrigerara)  iii  exteriore  (uperfi- 
^  j^  cte  cohsrct  firnnflime ;  at  fi  cn^t  frangatur ,  in  qoatn 
lacrymc  hcc.definit ,  ilUco  in  minufiora  frui^lt  dfifTot- 
vttur,&  feri  in  pnlverem,  qoi  ad  (patium  trtbus^arN 
>doque  pedibns  mains  disitcitm:.  Cnjus  phatnomeni  nh 
lia  congcua  m  ciidilory  advcrtcrc  invat  tum  Mmrioto^ : 

£  4  frafti 


7S  SiStU  I.  CaputtL 

frtfta  cuif  ide  non  «fiwlias  diifiiire  kerymtm»  fi  oidtm 
•  fuinnto  tlio  calore  y»cf e/^wVefrigerctur  in  aere.  fldo 
Cqne  dtflSHre  lacrymam  in  vaeuo  Boyktma.  ^cio»  fi 
qu^  iaerycnc  ope  fmiridis  £it  magna  capttis  (bi  partc 
abradantory  davenietiir  ferc  fcmper  ad  caviuten  aK- 
qum  baliarum  majoj^um;  quo  cafii  rompnntQr  plnri^ 
iQtfy  maxime  fi  pulvis  fmiridis  eft  crafliuCculus.  In  eat 
vtro,  quc  non  rompumur,  in&ratur  cufpis  acut,  &  aii* 
-quc.rurnpemur  illico  ad  concaQam  i  ali«  tardioa  retni* 
fia  jam  icu. 


« 


.  fb^mfrtimfi  'fic  txpUcatur  X  Molecolit  fninimis  la«  • 
crymam  componentibus  itiieft  vis  repuifiva  agent  in  illis 
intervalUs,  quiboa  diftabam  iix  moleculx,  quatidQ  txter^ 
M  fufirficies  fuit  tmftriSa^  Dicts  h  Didc  moleculft 
eodem  modo  ab  invicem  diftant  eujfide  imegra  petii* 
ilente ,  atc|ae  drffraSa  ;  ergo  fi  non  difliiium  lacrymc 
cufpide  non  violata,  neque  ob  difiantiam  difliliem  cu(|>i* 
cle  frada.  ]J2*  D.  A.  Eodcm  modo  dilUnc ;  intcgrt 
tamen  cuQ>ide  perfiverat  imptdintetttum  ^  qiio  minus  vif 
repuiiiva  cfFedum  fbrttri  queat  C.  A.  non  perfcvcrat  N; 
A  &  Cm*  Dum  iacryma  Batavica  multum  priul  calc* 
facla  r<;;ye»r«  rQ^/gertffiKr,  confl:ringitnr  exterior  fopieKli» 
cies.  fyja  bac  conflriSthntt  continencor  minimsc  mole* 
culs  veluti  ergaftnlis^quibusdam  inclufis  ,  ficque  impt^ 
Jiumury  quo  minus  alit!  alias  repcUere  poffint.  Dices 
IL  Moicculs  lacrymam  componentes  eodem  modo  di* 
itant  ante  rcfrigcrationcm ,  quo  jam  rcfrigerats  ;  ergo 
fi  prius  non  diilolvcbantur,  neqoe  refrigeratar  diflolvi  de« 
berent  cattfa  diflantia.  DiflTolvuntur  autem ,  ac  disji- 
ciuntur ;  ergo.  1^«  N.  A.  Ance  refrigerationem  cu 
lcbant  (umme  ;  calidc  rariorts  eranc,  qnam  frigidc'; 
imo  frigore  etiam  ctfideufaiauiur.  Ex  raritate,  ac  dcn^ 
fiCate  inferri  debec  diverfius  diftantiarnm  ;  ergo.  Oir 
•  aes  IIL  Lacryma  plumbo  liquato  immerk  cenn^  pellicu- 
la  obducituTy  nec  tamco  diffilic  rupca  cnfpide,  (cd  quo« 

lUm  modo  lameUftcim  findicor  ftdione  id  Jongitodi^ 

ncm 


fitm  lacrytnc  fere  normali.    Hidetfi  iutem  «ft  diftintit 
moleculanim ,  feu  lacryma  plumbo  immcrgatitr  ,  fivc 
sion' ;   ergo  rel  utrcbique  f  vel  uuUibi  confcrec  diftintii 
ad  dis)iciendas  particulas.        9»  Finditur  lamellatim  ^ 
quia  propter  plumbeam  pelliculam  lacryms  obdudiin 
impeditur  Ijberi  molecnhrum  disjefHo  in  omnem  par* 
tem«     Forte  eriam  particuls  ad  eam  dtftantiim  d^lit« 
iton  (unt,  in  qua  sque  operetur  vis  repuUlviy  ic  ilias« 
Jiices  IF.  Si  ope  fmiridis  lacrjrmarum  caput  in  tabuh 
metaUina  atteratur,  non  tamen  difGliunt,  quiritnmvis. 
artritu  tolUtnr  iHa  partium  conftri6>io ,  &  coarfiatto  ^ 
quse  diffrafiiohem  impcdiebat ;   erga  ncque  rupti  cu« 
Ipide  diflFriHgi  deberent.     1)2.  piflilkint  plurim^..  Qaz 
non  di(Gliunt,  partes  habent  non  eodero  modo  conftri- 
Aas  in  nodo,   (eu  capite,  quo  in  culpide.     -^.  adot 
Neque  omnes  rupca  cnfpide  dif&ifiigiinmr.     19t/|tto: 
Eadem  difflctiltas  manet  adverlarios  omn€s  \  (eu  igttem 
ifti ,    ieu  Mrem  inclujiim ,   aut  extrinjicus  irrumpentem 
phxnomeni  caufim  pronuncient.    Sed  omniiim  redifli- 
me  nos  difficulratem  iftam  diflblvimns ,  quibu»  vis  r€- 
pulliva  in  certis  diftantiis  agens  difTradtionis  hujus  caa(i 
dicirur.     Cur  enim,  quse  attritahon  diflilionti  sn(erti 
«cuscufpide  difFringuntur?  mutatnr  nempe  diftantia  ^ 
«aque  mutata  agit  vis  repulflvi,       Dices  K   j4er  iuclt^ 
fvs  iiitra  laerjmas  illam  partium  disjedionem  operatur; 
^*  N.  A*  Hic  edlim  rariflimas,  ac  proinde  nullius  (ei^ 
Itbilis  effeftus  capax  erat,  cum  interdperetur  ;  lacrymae 
cnim  ealebanffumme.     Dices  VI.  Proinde  ab  aere  ien* 
fiort,^  extrinfecus  fra&a  eujpide  irrumpente  effeOua  ilic 
repeti  poteft.      ij^.  N.  A.  Perindc  enim  diftringuiuar 
lacryms  in  vacuo  Boyleaup ,  itque  extri  iftud,      Dicet 
VIL  ht  igni  tribui  poterit  phcnomenon ,  qua(i  ignis 
in  motn  quQ^am  con(ervet  particolaa  latiora  (])atia  po« 
feentes.     ^.   Si  lacrymc  n<m  r^ferata  diflilireiitt 
dici  ifiud/tfr^e  poflfct.    A  refrigoritis  j^ridcm  Ciio^  m^ 
%vm  fui  partc  in  aoras  abiit* 


%X' 


XfXy 


Seaial.  CipatJr. 

III.  j4tfipulla  BQmniinfis  non  mmpitur  iiijeAo 
tr.  jr.  plumbifruftillo;  ac  iinininb  fiiicis  fragmento  diC  ^ 
(iHt  ad  bafini,  alias  ferendts  malleorum  i£iibus  idoaeatfi. 
Scilicec  •*  acie  (ilicis  (juzdam  molecuis  fuperficieiii  C4- 
vam  (ormzntts  JipMrautnr  ;  mulcoque  rutupuncur  faci- 
lius,  quam  impafi^  cujuscunque  cerporis  alcerius  mot 
liorist 

Schol,  IL  Adverdis  noflram  banc  de  alttrnacione  ^ 
virium  doclrfnam  Jblent  ^  iJlud  objicere  (  icribic  Bosco- 
vichius}  in  hac  fotijjimum  tbeoria  eommitti  faltum  ^  ad 
quem  evitandum  ea  imfrimk  admittitur  t  fieri  enim 
tranfitjum  ab  attraSuinibus  ad  repulfioues  perfaltum^  ubi 
nimirum  a  minima  ultima  repulfione  ad  miuimam  prU 
tnam  at^raBionem  tranfitur ;  &  vicifnm  ;  ergo«  9,. 
N.  A.  Salcus  admiccicur  ,  cum^ab  una  magnicndinc 
traniicur  ad  aliam  iine  cranlicu  per  intermediat ,  quod  im 
cafli  prxfente  non  fic;  tranfitur  cntm  a  y{  repuKiva  UN 
cunquc  parva  pcr  omncs  incermedias  vires  rcpuKivat 
minores  ijfque  ad  zerutn ;  tum  primum  devenitur  a4 
vim  atcra£tivam,  qus  per  omncs  icerum  gradus  a(ccndie 
^fqiie  ad  decerminacum  quemdam.  Dutnquc  a  poftre* 
fno  reputdonis  gradu  itur  ftd  primum  actra£^ionis  ,  ad- 
liuc  cr^n(ttur  per  incermcdium  zerum^  five  limicem  vi» 
rium,  nihilquc  incermcdium  omictitur.  No/fer  iUe  do» 
cer  nonhabQri  in  viribus  ullum  gradum  jprimum,  aur 
poftremum ,  ficut  nulla  dacur  ordinaca  poftrema  ,  auc 
prima  ^  nuUa  lincola  omnium  minima ,  cum  data  quar 
cunquc  lineola  uccunque  cxigui  alia?  habcantnr  mino-, 
rcs )  &  minores  ia  infinitum  fint  uUa  ulcitpa ,  in  qua 
ipfb  rcpeficani  cfTe  aic  concinuitacis  nacuram.  >  Objiciunt 
iterum  :  Attradio,  &  rcpulfio  fiint  divcrfat  vivium  Cpe- 
cics ;  (atiu^  crgo  forct  altcram  dontaxat^dhiberc ,  & 
repulfionem  explicarc  per  minorcm  attradioncm.  |{t* 
T.  A.  N.  Cnit  Divcrfa  (pocics  nihii  obcflTcc  attrafiioni^ 
^  rcpulfioni ,  cntii  poficivo  argumento  evincicar  utrap  . 
^^'    ]Q2«  ado.  N.  A»  Utraqttc  vii  pcrcinel  $d  aaudem 


Jpecitnty  cnm  repuKto  reJftBu  MrMonU  negitira  fir ; 
negativ^  autem  a  pofitfvU  nm  diffiruue  Jpecie.  Dixi : 
ripui/t»  nig^tiva  e/i  refpeSu  attra^iouis.     L  quia  oritui.*' 

Set  QontinQiin  fiibtra^iQnein  ab  atrradione  (  qtue  qui- 
ei^  (ubtraftio  fi  Hac  ad  zeram  a(quc,  nondum  habctur 
repuKio,  (edpoftea,  auod  diligenrer  adverti  cupio)  . 
EvC-  6t  formula  Algebraica  :  4«  -•  x  =s  z  (x  au* 
^rcm  valeat  primum  10,  rum  ao,  30^  40,  50,  6.p  &c. 
ifSfis  z,  valor  eruetnr  )  •  Fiet  40  --*  10  =3  ^o  ; 
#0  —  ao  st  ao;  40  -<  JO  =3  lo.  Hattenat  ha- 
kerrrar  immtnuit  (emper  trtradio,  Si  fiar  40  "^  4^ 
p:  Q|  nequeattra^liatiahebitari  neque  repnlfio«  Por- 
fofit  4Q  -«  50  =s  »^  »10;  40  —  60  =3  —  ao&c^ 
babebicur  repulfio.  U.  Negativa  ell  refpedn  attraSio'' 
«ar»  quia  diflTert  ah  9^ttra(iione  per  fo}am  direShnem  e 
4iametro  offtofitam^  non  ^ui  atque  accefllis,  &  receffiu 
(iba  e  diametro  opponuntur.  X»^  ramen  vere  pofitivti 
eft,  pUn^  irerum  ficur  acc^fTus ,  &  recefTus.  Dixi  \U 
Kegarivil  w»  irffertm  Jpecie  a  pofitiyu ;  oriunrur  enim 
fx  coiidna»  fi]btradione^a/&^or»m,  qu9  uciquc  futtt 
fjn^4^  Jl^ciei.,  Hine  vera  niBqcie  repulfio  (pecie  differc 
ih  attra£tione.  Adde ;  quod  lildem  legibus  Ofcr^tut 
ti^a<|aQ  itk  mimmM  difimtiif% 

^.25.  Pars  7  /«  mAJorthut  ^ijianfiu  virejtjifnp^ 
filfit  anrn!fiv4  ^ffntcs  ai  finfiim  in  rgfion^  nciproi^ 
^n  Juplicgi$4  MJlmtiarum^  Carpor^  ^nfrn  terre-^ 
ilria  omnia  graviram  in  ferrim,  planerap  om* 
Pf%  in  (oleaii  ima  ocnnia  m  («  Ce  mtuuo  gr^- 
f  iranr,  in  omnibus  haberqr  s^tirminatiei,  ad  mu^ 
pium  accfjfHm.    Se4  d<^  hoc»  iremque  de  racia<« 


CA^ 


iS  SeBhl  C<^nT, 

Gaput  III. 

De  Curva  exhibente  Legetn 

•     Yiriun-# 

.  §•  24«  Familiare  eS  Phylicts ,  res^  qair«^' 
rum  idea  adventitia  \  ac  intuiriva  baberi  non 
porefl,  in  fymbolis  tanquam  in  imagine  ex- 
tiibere »   iit  facilius  ope  idcx  (ymboltos  co* 
gQofci  poflinn    Iftod  ago  ex  Bpuovicbio. 

$.  2y.^  Totam  virium  legem  exhibet 
isniCa  iimpliciffima  curva  (Fig.  2.)*  ^^  Q^f 
(pumprimis  notari  merentur  areus  curvj^.  fido 
ar04^  quas  comprehendit  axis,  &  arcus.  3110 
jfunila^  in  quibus  curva  (ecat  axem,  ySii  limiUi% 
Pc  bis  poftea ;  priusenim  alia  memorabp, 

SehQk  Juvat  inodam  conftrnendc  iilias  corrs  cx« 
«ofuiflc*  Aflfuinatar  (  Fig.  cad. )  linea  qaspiain  indc* 
finita  ^C,  fld  cajus  [Nin^um  ^.crigfltar  pcrpcndica# 
fum  j4B  indefinitc  mflgnum  ,  &  i^mptotkum  carvct* 
Ex  punflb  fldmodam  vicinis  pundo  A  crigantur  denuo 
pcrpendiculfl  ag^  bi^  &  aHa  quam  plqhma,  qa9  in 
figura  qaidom  cxprcfta  non  fiint,  at  rabintcliigi  dcbcnt ; 
^  ca  legc  crigantor  ,  ut  fint  in  rmioue  reciproca  fihtpH* 
cir  diflantiarum  a  pando  A ,  flve  ut  hoc  maios  fit  pce» 
pcndiculum,  quo  minor  fiicrit  diftantia.  Fict,  af  im* 
minutts  diflantiis  cre(cant  pcrpcndicula ,  aoQis  dccreC 
cant,  dum  fubinde  in  pundo  aliquo  C  cirancfcant. 
Ildo.  A  punQo  £  dimittantur  pcrjicndicnla  ib  &c« 
qux  a(qae  ad  pandum  F  cre(cant ,  tum  otqac  ad  G 
i^crffiata  in  rmm  wm  ^i^  V^  Jihyhee  inverfa  dU 


lixvirium.  77 

jhntifgmn,  Illtio.  Efldeni  lege ,  CcA  eppoJlt4/9L  MtttT'' 
nantedireSioM  exdtencur  pcrpcndicala  primam  ercC 
centia  ufque  ad  diftantiain  aliqlram  f/,  l^  Af,  O,  ^,  S  ; 
mox  decrefcenda ,  &  evanefcegtia  in  punAii  J,  £,  >( 
iP,  S.  IVto.  Excitatis  hunc  in  modiim  perpcodicnlis 
«{qoe  ad  puqfhim  aliquod  axeos  a  demittantur  ex  c»* 
dem  punfio  •  pcrpandicdia  a  p  ,  v/,  vcrfiu  Cy  fed  m 
TMOHi  reciproca  Juplicata  difiautiamm  A  v  ^  A  %• 
^Vto.  Per  (ingalorum  perpendiculorum  cxtremitatef  f, 
#,  &c.  ducarnr  curva  fluxu  cominuo  DEFGHI  i 
L MNO PHRS TV.  Dica  t  Iktc  cnrva  txb^in  tu 
gtm  virium.    Qaod  ritc  at  inteliigatary  (ic         ** 

$.  z6.  Axif  cfxrrtt  huius  eft  linea  indefi* 
fttta  iitcunque  magna  A  C  Servit  notandis 
punAorum  materiat  difiatttiii^  &  obftrv^odis 
ordinacarum 


§•  27.  Orditiau  €\xnt  Iine«  vtlStx  aj^^  ht^ 
Ji^  il^  mtt^  tz,  uy^  a^,  vs^  &  harum  li- 
miles  aliae  pirpcttdicularei  ad  axem ,  &  m  curvs 
perimftro  termittata.  Referunt  ordinata  vires 
lubinderir^^vtfi,  fubinde  attrgHivas\  &  \\\m 
quidem ,  quat  in  arcu,  vel  CTare  fupcriore  ter« 
minamur,  fignificant  vires  rcpulfivas  ^  e«A 
^j»  ^^1  ^^9  ^^i  quxinarcu,  vel  crure  if§m 
Jcriarty  sttraSivas  ^  quales  funt  di^  il,  uy^op^ 
Vi.  PolTunt  vero  plurimx  aliae  ordinat»  diici 
a  ^ngulis  pundis  axeos  ad  quemcunque  ar« 
cum ,  ut  patet  $x  ffnefi  curvarum  ^  qu«  tp{k 
ordtnatJT  jam  augebunturg  jam  minuentur^ 
ittcremcntum  hoc »  &  dccrcmetitum  ordinatarutn 
fignificat  augcri  vires»  vel  immitiui^  prout  curv^ 
ad  axm  accedit^  vel  jrecedic« 


7%  ScSwL  Ofntm. 

f.  2g.  Abfiijfa  Cnm  regtnenta  axrs^  ad 
qpem  refercur  curva.  tn  figura  noftra  line« 
Aa\Ab,  AB,  AJ,  Ai  &c.  abfciffit  funtw 
Deftinantur  vero  abTcilHe  fignificamiis  diftan^ 
tiis  duorum  punAorum  ab  invicem ,  qaorani 
altenim  femper  in  punAo  A  locacur. 

ScboL  Hie  iam  (edalo  adverrendom  i  ibfciflb  wu^ 
w  ab  ^  ufque  in  K  perdnere  ad  difiiiidaf  temper  id* 
boc  miuimas,  rcliqoas  td  majores.  Qciire  ibicifli  Aa^ 
vel  Aff^  A Ey  AdOic.  figiiiiicit  diftannas  c.c.  oiole-> 
cularam  (cn(ibilitcr  condnuirum ,  vel  contiguirnro  : 
iMcHTa  vero  Ao^  Av  diftantias  corponun  remotiorumi^ 
&  in  (e  mutuo  gravitannom ,  v»  g«  corporum  delaben» 
tium  in  terram,  aut  planetarum  gravitantlum  in  fi)lem« 

^,  29.  Crur4  duo  attentione  omnt  dtgnt& 
fima  funt :  primum  DE^  alurum  JpsV.  Crus 
DE  pertinet  ad  folam  vint  repulfivam^  agentem 
in  minimis  difimtiii  in  ratione  rectproca  fimphea 
diftantiarum.  Crus  TpsV  fpeAat  ad  (blani 
vim  dttraHivam  perpetuo  agentem  1«  maj&ribuf 
iifiantiis^  &  agentem  in  ratione  reciproca  du* 
flicata  diflantiarum.  Ambo  crura  afymptotieis 
funt,  qu«  nimirum  fi  indefinite  prpducantur 
ultra  quoscunque  limites,  femper  magis  ao* 
cedunt  ad  redam  aliquain  itidem  ultra  quos* 
cunque  limites ,  quin  unquam  ad  eandem  de« 
veniant.  Atque  primus  ille  arcus  D£  (emper 
magis  acceditad  redam  AB^  nec  tamencum 
ea  concurrit ;  pofterior  arcus  TpsV  ad  redtam 
A  C>  h.  e.  ad  axem  ^  quem  pro  afymptot^ 
habet«  ]  ^ 


Itx  virium.      ^  ^9 

Schol  t  Ordimtit  rcferont  vircs  f f  2^; ) rMfdf 
fa  diftantias  (  ^.  «7«)  •  Quarc  (Tnsf  2>£  perrinens  ad 
felam  vim  repniiivam  flgentem  in  minimiidiflantiis ,  flt 
ff/  ratiotie  reciproca  fimplke  difimtiAnim  erit  crss  i^ 
perbola  communif ,  cujas  nfymprotus  (it  yi  B.  Ramns 
vere  TpsV  pectinens  ad  (blam  viitt  attra^ivani  agen* 
tem  in  miij0ribns  dilhntiis  ^  &  in  ratione  reciproca  dti* 
fJieata  diflantiarum  erit  ijyperbolicus  yii  gradus'^  cujui 
**  tJ^infiotus  fit  axis  jIQ 

.» 

JiTi&s/.  11$  Dixi  t  crus  prinmm  D  E  efle  cras  i&y- 
periiia  comntunis ,  crus  autem  Tps  V  cffe  hyperboU- 
cum  gradus  ^tii.  Utrumque  p^tet  ex  eo  ,  quia  in  hy,- 
pertoJa  commuui  ai  ajymptwm  relata  ocdiBaic  {unt  in 
ratione  inverfa  fimplice  ablciflarura  ;  iu  ifyperMa  vor« 
jtii  gradus  itidcm  ad  a/ympsa$um  relata  funt  in  rationt 
reciproca  duplicata  abCcinarum^  Ipfum  hoc,  ut  diicipu* 
lorum  quorundsm  dcfidcrio  iatisfaciam  ,  breviter  fic 
oftendo  1  Demonftratum  eft  (  a  Cel.  JVolffio  Elemenu 
Matbef  Tom,  L  in  Elem,  Aual.  N.  4S7.  &  48S. ;  item 
t  CL  de  la  Caik  iu  ie&iofi.  ttlem*  Matbem.  N.  870.  St 
%7V  )  quod  in  byperb^la  commnni  ad  afympi^nm  refm^ 
ta  (it  re6langulum  ,  (eu  faOum  ex  ab(cifl*s  ^uacnnque  \vi 
iemiordinatam  ruam,  parallclam  iid  latus  altecnm  af^m^ 

ptotienm  cqnalea  (voco  aiQtem  a  latus  CR^  vel^R^ 
eajus  quadratum  potentus  byferhofte  dicitur ;  vide  Wolfi' 
fium  ikid.  N.  477.  )  •  ^  Sint  {emtgrdinat»  GE^&  HR 
(  Pig-  h  )  7  quarum  prior  vocetur  y ,  altera  «•  Sint 
fcmiordinatis  refpondentes  abfcink  C£,  &.CF^  qut* 
rum  prior  dicatur  x  ,  poftcrior  s.  Qnia  aquatio  natu» 
tfm  byptrboU  comimunk  intrk  ajyfnptotos  deelaraus  eft  s 

9jf  ^  ss  (  ut  panUo fiipff a  dianiii  ex  IFo^,  &  de  U 

Caitte)  ^  babebitttr  etiam  srquatio:  tu  ^  a  ;  ac  pro- 
inde  xy  ::*  zu  (^.  t.  axiom.  4«)  .  Fa£la  jrqualia  CoU 
vendo  inproportioncm  fiidorcs  rcciprocando  fiet  s  jr ;  k 

:iS 


9o  &ahlGfutttJ. 

ts  Ht  >  1m>c  eft :  ia  bjrperboii  coinfnum  ad  ftfym- 
ptonim  reltu  (cnnordlnats  (anc  in  ratioHe  snvcrfa  J&jg^ 
pliee  abfcifliinimi        Eft  vcro  irerQm  trqmtio  natnram 

IfyperioU  $tii  graim  intra  ajymptotos  dularam  x  y  =:  ag 

Ergo  eadem  radone  nct  t  z  a  =:  a .    Proindcque  x  y=t 

z  u  ( $•  &  axiem.  cit. )  •     Rurfiim  lolvendo  fa^  arqua« 

lif  in  proportioncm  habebitur  yiu  s  z  :  x  i  id  eft  ; 
sn  hypcrbola  tertii  gradua  ad  afymptotum  rclata  ikftiu 
ordinatx  (iint  imrationc  reciproca  duplicata  abrciflkrum* 
Q.  £•  D«  *  •  i 

^.30.  Jbrcu$  diftinguendi  funt  in  rtfUlJU 
vot )  &  0tra£Hvof ,  prout  nimtrum  W/  , '  vel 
trant  uxcm  jacent..  Repulfivi  (unt  fuperiores  : 
0itraSlivi  inferiores.  Deftinanturiignificandae 
^anut4ti  virium  attrabtnHum  \  vel  rcpelUntium  ; 
cum  enim  per  ordinatas  fuperiores  exhibean* 
tur  vires  repulfiva  ^  per  inferiores  attra^Siva  z 
qao  ma|Wes  fuerint  ordinat»)  hoc  major  yis 
exhibebitur*  Majoribus  autem  ordinatis  re« 
ipondere  debent  majores  arcus  (  cum  arcus 
concipiantur,  oriri  e  Tertictbus  ordinatarumi 
infinite  vicinarum  certa  lege  crefcentmm  ^  fic 
decre(centium  )  ;  ergo  fi  per  diverfitatem  or« 
dinatamm  exhibetur  dtver(a  ouantitas  vipiuni 
ieu  attraAivarum  »  (eu  repuliivarum  :  exhl*  - 
bebicur  itidem  per  diverfitatem  arcuum« 

aroB.  l  Hinc  tnritut  alla  diftin£Ko  artttum  tn 
mugores ,  &  minores ,  qux  (blicite  ob&rvanda  eft.  Ma* 
}or  arctti  cft  €•  #•  G^Z,  mioos  Xe^Tt 

CeroS» 


C^oU.  IL  Si  carva  fecsbit  axf  tn  fere  perpendkulg^ 
ri9€r^  &  dein  Unffffifne  ab  eo  recedet ,  n  ox  vivin^  in^ 
tsrledioni  crdiuautf  &  per  ordinatas  rcpisfentat^  v/rcf 
•dinodttm  magnc  babebQntor. 

^  jT.  31.  Magnopere  irepi  cur^nda  efi  di« 
firibacif»  «fCQum  tv  mrfUorii^  Ctu  vaftioret ,  8c 
jmmt  0tnph/^  AmpUons  voco^  dum  pundn 
multum  licec  a  («  receiiefitia  ob  adhibitam 
vim  extriniecam»  adhuc  tamen  manentTub 
eodem  arcu»  qui  dicirur  efle  (atis  vailus.  Mim 
nus  dmfti  fisnt  ^^  a  quibiia  pun^a  ob  urgenteoi 
vim  extrin(ecam  a  (e  (^  recedentia  deveniunt 
ad  alium  arctim.  Imago  arcuum  ampliorum 
•ft  arctts  L  M  N  f  ytl  L^if  i  arcaum  minuf 
amplonim  P$f.     ) 

CoreS.  FoAitnt  ergo  aftdf  mkiaf  ampK  tffk  ftu 
Mentiffimi  in  corporibvf ,  imo  re  vera  (iinc  admodani 
frcyiieetef  Ut  imUihm^  m  <|oibus  tra^fcurji  limitt  na$$ 
€9bitfionis  ficile  devcnitur  ad  Urftium  cohafiQtiis.    \ 

ScitoL  Pi^nt  criam  arcns  ita  occarrerc  axi ,  nt 
com  &lummodo  tangant,  aoc  vero  dyntaxat  ad  viciniam 
aocedant»  mox  recedant.  Vide  arcum  Pe/.g  R*  Atquc 
talis  erit  curva  ,  (i  quando  fuerint  vires  iii  minimis  dt* 
ftantiis  decrefcentes,  mqx  it«rum  crefcentcs,  quin  trana» 
ieriht  ad  oppofitss. 

§.  sa^   Jrts  comprehen&  arcubus  \  8C 

axe  curv^  exhibent  fuaJrata  ctJtritatum  a  viri« 
bus  ip(]s  genitarum»  &:  a  dato  pun^o  five  4^« 
quijkarum^  feu  am^arum.  Sedkione  proxima 
aemonficabo,^  quemadmodum^  fi  per  reiftani 
referentem  fpatium  alia  ducatur  reda  exhibeni 
vire^areageaiudefignet  quadratum  velocitatis 

F  Sdak 


r 


8»  ScSki.  c^m. 

^ScboL  Long^  fim ,  fi  area^  oinrarqfii  inveftigare 
doceam.  Ifiod  brcviter  adnocabo :  aream  cmre  D  E, 
&r  ajymptoto  yiB  ^mftprtbefifam  infinhav»  offe  (  qaja  AB 
«fyroptorus  eft  )  adeofm  foi-em  exfiinguewLe  cnivu  veU» 
ci$asi  offofiut  uteuuque  majffut. 

§-  3  3*  •  TbiorenMM  ad  areas  cunrj»  hujus 
periinentia  fere  fisnt,  quflB  (eqountur : 

!•  Si  punSum  quodcunque  fnovuuur  direBiona 
icnfpirante  eum  vi  punSi  alterius  in  A  loeati  ^  ac-- 
auirit  eeleritatem  mvam  s3  rsdici  area  rejpondenHi 
jpatio  percurfi  (conCpir^nt  autem  direAiones  fub 
arcubus  mtraUivis »  fi  pundum  unum  mfdat 
ad  aliud  ;  conlpirant  etiam  fub  reptdfivis^  fi  r#->. 
Mat  ab  alio}  •  Jam  fit  (patium  percurfiin» 
•bfcifi^a  E  G ;  huict  8c  arcui  infiftenti  refpon-p. 
<^ns  area  fignificaiHt  quadratum  velociratis 
i§.praced.);  h.  e.  fi  area  dicatur  x^  8s  celeri*^ 
tas  c ,  erit  x  s  cc^  quare  utrinque  extrahen» 
do  radrcem  fiet:  y  x  z2  c.  Hanc,  inquam, 
celeritatem  acquirit  pundiim  motum  dirediono 
sonfpirante  cum  vi  pundi  d ;  quia  enim  fuppo^ 
tiitur  moverl  verfiis  pundum  if  celeritate 
quacunque  e.  c.  xa»  ^uam  vi  inertias  confer- 
Tat ;  fimulque  determinatur  ad  accejfum  verfiis 
idem  punAum  A^  v\  fi:ilicet  attrahentis  ejus« 
dem  punAi  A,  necefle  eft,  novdm  jub  arcidm 
MraSivis  acquirat  celeritatem  s:  Y  x 

Corott,  Ergo  Pandum  qnodcunqne  accedent  ad 
aliad  fiib  arcubns  attra&ivis  novam  iemper  acquirit  ce- 
leritatem  s  Y  *  #    f  ra|iudequc  tota  iUiius  celcritat 

««iiY*. 


Lex  vlritail»  8) 

IL  SS  jmnBum  auod,cun^ui  Moveamr  SreBio* 
ni  oppojiu  vi  pun£li  A^  amiuit  aUritatim  :s  radid 
arcM  nfpondiTUis  /patio  ptrcurfo ;  Dam  cum  fup- 
ponatur  urgeri  dircdione  concraria»  debec 
proptcr  excipientem  vim  concrariam  ceieritas 
prior   eoufque  elidi  ^  dum  celeritas  amifla 

Gr»ff«  L  Panft vim  qiiodctinquc  aaeiens  ad  alliui 
lbf>  areuhns  'rtpulfivis  aliqaam  (emper  amictit  celericia« 
ttm  :=3  Y  ^ ;  quare  tota  illins  celeritas  emcn(b  )am 

Ipatio  c.  c.IGs3c--Vx. 

• 

CaroH*  IL  Pnndam  quodetinqiie  reiedtns  tb  alio 
fiib  arcabus  nfuJfivu  novam  acquirit  celericatem  (  quta 
diredio  pundi  receientu  con(pirac  cnm  vi  fub  areubus 
repulfivu  )  ;  (ub  atcradivis  autem  amittic  aliquid  veioci- 
tacis,  quia*dire£lioptm£li  r^c^^fff^j^  pugnat  cum  vi  iub 
arcubua  attraSivif. 

IIL  ^  Si  punSlum  moviMur  per  majui  Jpatiam , 
€ui  njpondiant  ans  ^artim  attroBiva ,  partim  rf- 
fulfiva^  fubtrabatur  Jumma  aiiritatum  amijftntm  4 
fimma  eiUritatum  aafutfitartm  ,\  diffinntia  dabit 
iikritatim  toto  iUa  fpatio  vil  navitei^  acquifitam »  vA 
mmjfam  ;  e.  c  pundum  aliquod  in  R  conflito- 
tum  movedtur  ufque  in  E  impuirum  celerita* 
te:=:  12.  Sub  arcdbu^  repuliivis  PC^R» 
L  MN^GHI  amittat  velocitatis  gradus  2t  »f«  3 
ijh  4.  Sub  attradivis  N  O  P,  I  K.  L,  EFG 
acquirat  gradus  3  4*  4  4*  5 ;  ^rit  celeritas  to« 
to  fpatio  E  R  aequijita  ;=:  12 -<  9':=:  3;  pro»* 
iflde  tota  illius  ccleritas  :=:,  ittiff^^  15« 

F  »  IVJ 


S4  SeBht  Caputllh 

IV.  Si  In  cojfu  dir^Slionum  oppoJHarum  V  x 
f^c,  punHum  exRinP  motum  citius omncm  ccUru 

iatcm  fuam  amittct^  ^uam  devcniat  in  P.  Sit  c  ^  6^ 
.&  V  x^  9*  Qpia  in  cafu  mocus  oppofiti  ba- 
bctur  tota  cclcritas  =  ^-^  Y  x  ,  fict  ^—  Y  x 
s:  6  —  9  ss  —  j,    proindc, 

Cdroll  Crgo  (i  punQnm  altquod  ab  E  moveatur.in 
/^y  c4ericas  iUims  ,  ^aantacunqae  fit ,  privs  exlKngoi 
ddbff,  qoam  perveniat  in  ^^  cum  ^im  ar^  crore  D  £, 
^  ^fymptoto  ^  j8  cofnprehcn(a  ::;;  oo  (  §.  ^hSchl.} 

erit  (emper  Y  arex  illius  fnajor  quacon^ne  celcritatc  fi* 
nita  otcunque  magna.         ,  :- 

V.  Si  in  cafu  MreHionum  confiiramhm  punm 
ftum  4ju(fJcuniju$  ingrediatur  aream  repul/vdm 
emnino  ingcntcm  (  quac  fupcret  rcltquas  oppofi« 
t^s  arc^  omncs»  &  in  qua  limcs  alter  ab  alterQ. 
plurimuro  diftat )  rccedct  fine  fine  \  nam  ccUri^ 
tasfub  arcu  iUo  inienti  aajuifiu  ponitur  nunquam 
cxuinguenda  (bb  areis»  6e  arcabue  oppoutis. 

*  ScboL  Theorema  hoc  afui  eft  in  explicanda  lumi* 
ttis  cmiflione,  &  aniformi  propagatione  per  iminenfii  il« 
la  inrervalla ,  qos  terraoi  inter,  &  fteiliia  fixas  iaceic^ 

VI*  $i  punBa  duf  eadem  direRionei  at  diver/h 
VeUcitatibus  acccdentia  ^  vcl  rcccdentia  eSf  codem  ali^ 
quo  punSlp  ingrediantur  arcam  iterum  innntcm  ^  ean 
dem  pre  veUcitate  exibunt ;  nam  poflT  accediq* 
nem  illan)  novam»  qus  fub  ingcnti  illo  arca 
ficri  dcbct^  vclocitates  corum  parum  difTcreht; 
ficut  fi  quadrato  niagnx  cuiuspiam  radicis  ad-^ 
datur  quadratum  aiterius  multo  minoris »  &  e 
fumma  extrahatur  radix  |  non  mqltum  difieret 
radix  fummm  a  jadice  quadrati  majorii^ 


$.  94»  Jain  de  PimAis*  futASj  in  ^ui^ 
hut  curv4  occurrit  axi^6c  ordtnatc  fic  (rTaneAsoni^ 
|it  macent  dire&bnem,  dicuntur  limiM  virium. 
Duplices  ii  {Iint  :  cokefionii^  &  mn  cohafioniu 
Limiut  cobdjionis  pun<^a  iunti  in  quibus  cre«» 
icente  z  pmAo  A  diftantia  tranlitur  a  vi  n* 
pttijtvA  ad  attradivam^  e.  c.  in  E,  /,  N.  R.  Limi* 
Ut  non  cobafionis/in  quibus  auAa  iterum  diftan« 
tia  fit  rranfitus  a  vi  attraAiva  ad  re^Hiliivam ^ 
ut  in  G,  L,P. 

SchoL  L  Limkit  edhajtoilk  (isnt  in  ^vt  ntiitKro-. 
rttf;n  imparium  i,  ),  ^»  ?•  Lithitet  non  oohafimtt  ia  fi^ 
m pAriam  1,4,  (.    Vi^e fig. tit. 

ScM.  It  VtriqiK  limkes  poflimt  jn  itideffleof;^ 
ftbtis  cHb  adtrioimn  /hquinmt  (  Cmpor  tameti  fVi  i/i« 
fimtiis  adbnc  pwUmis  )  ut  fit  in  cdrporibus  motliim  ; 
«at  tongm  a  /e  difiantet,  ut  fit  in  ehflicis.  Fofllinc  e£ 
fi  rrequenteSy  certum  efiim  habei^us  ex  Geometri^  cur- 
Vam  pafle  axi  odcurrere  tn  quctcunque  punSft*  Etiat* 
longiusf  dtftsf tf  poifitnt,  etttti  ttkkiti  eerttim  fif  Him  poi% 
^cv^tttt  i»  ^uikipltftifUlt  fkuOit* 

§.  35.  Llrnites  cobedonis  atii  font  fortip^ 
fitm,  langmMortt  alii.  Vaiidi$mi  (unty  in  quibos 
xurva  Mcat  axem  fere  ad  {>erpendiculum «  & 
dein  longiifime  ab  eo  recedit.  Dcbilioret pint^ 
in  quibus  curva  valde  obliqoe  occurrit  axi^noc 
multum  ab  eo  recedit» 

CejraU.  Proinde  vis  InttiniiB  non  pendet  a  vklattate 
|mnd«f»m,  aut  4iftantt»  Umitam ;  ftd  (  uf  dia^i )  A  in* 
clioationt ,  lc  rec^o^  arcutom*  CevKf  tmrum  (  qood 
idemidiem  adverfariii  o{|arcndttm  )  vicinioret  habet 
liioleculas ,  derifius  eriim  eft ,  ac  %ecifice  grsvios ,  qnarti 
«^/Wi  firmioi  umen  non  cdtM^tmmtfn^  qosm  ifii- 


§•  9^.  Ad  limites  virittitt  pertilietit  hate 
cumpritnis  theorcmara, 

L  fuf^s  maurU  in  Ijmflffci/  ^whutcuncp^  J» 
cafa  (untih  a^uilibrio^ ac  prainJi comjuicjcuni^  In 
utrisque  eniit)  limiribus  eyanefcunt  ardtnarx^ 
wc  propterea  nuUis  ibi  viribus  panAa  urgen^ 
tur;  ergo* 

ScboU  CoHjuieJcttt0,  inqtrara ;  non  idee  iob^i^ent  in 
Jimitibus  uiHsqne ;  ih^hsfio  enin  ,  qaod  dlcam  c  4.  ^ 
lYOu  habetQr,  niH  punfls  iocentar  iniis  limitibuc,  in  qui- 
btts  a  repalfiane  tranfitur  td  attrftftienem^  h.  e*  in  limiti* 
buis  cohsfionis  (§•  n*)  • 

IL  Si  punihcm  dimovitur  s  timti  cohafianii^ 
tejfanu  aSiom  ixtrinjica  continuo  ndU  ad  Jitum 
fuum.  Si  entm  pundum  artquod  in  E  locatum 
vi  gtiapiam  exrrinfeca  urgearur  rerfus  A^  iti^ 

Sredierur  arcum  rcpuljivum^  quare  continuo  re« 
ire.  debebtt  cefTante  aiSione^externa  propter 
,vim  xepallentem  punAi  4.  ^i  verfui  G  ^  in- 
gredietur  4{ir4(3fz;icffii»  iterumque  redibit  pro« 
pter  vim  attrahentem  ejusdem  punAi.it 

SchoL  In  exemplo  fit  elaftram  chalybeum ,  cu}US 
extremitates  fi  addncantur,  cefiantt  comprsflione  ror- 
fum  naturali  fitui  reflituentur.     |tidf m  fi  didncantur. 

IIL  Si  punBum  dimovctur  ix  limiti  non  cobs» 
Jionii^cejfami  vi  ixtrlnjcca  non  re^t  ad  Jitumjuum. 
Sienim  punAum  in  O  conflitutum  dimovea- 
tur  verfus  A »  in^r^ietur  arcum  actrahentem 
£BG  y  6e  a  punAo  A  atrrahetur  verfus  £» 
S\  dimovobitur  ver{tis  />  ingredietur  arcum 
repellentem  GHl;  quare  ah  eodeoi  punfto4 
repclletur  ufque  itt  ii  '     . 


ScM.  »€•  tdambmi  pot«ft  l«r  gwiu  ptptwis  in 
tetnulum  congtfta,  qu«  in  limitibut  funt,  quamdiQ 
^uicfcunt ,  fcd  in  Hmitibus  mn  c^bafiortis,  nam  loco  di* 
mota  ad  fitum  fiium  non  redionAi 

IV.  ^unBa  in  limitibui  eobdfionis  hcaid  nfi^ 
fiunt  tamjui  comprijfioni^  quam  difiralHmii  nam 
ex  limitibus  iftis  dimota,  &  ccflante  vi  com- 

erimence,  aat  diftrahente  continuo  ad  priorem 
tumredeunt  (§.praf.pftor.2.) 

C^rott.  Quarc  mcrito  limitcs  i£U  cobafiww  limim 
diconturt 

V,  PunSta  in  limHihus  non  cobafionU  eonfiituU 
nee  fiii  comprejfioni  re^fiunt^  nec  difiroBioni  (  nifi^ 
forte  urgeamur  ad  immediatum  contaAum); 
fiam  de  loco  fuo  dimota  ad  priorem  fitum 
non  redeunt  ( Tbeor.  3. )  •  Excipio  taroen  re- 
fiftentiam  omnibus  materic  puniftis  conuna^ 
nemi  ^uatenus  inertia  funt. 

Coretti  Infeits,  cnr  Umitci  ifti  um  eoUfionis 

cantur» 


VL  SipunSa  in  eobsefimsis  Umitiius  confit 
§uri  fw^umquo  unum  de  fuo  hco  dimoveatur^ 
fuHSli  sdterius  motum  eonritari  debei  aiterum.  Si 
enim  pnndum  B  moveatur  cpotra  A^  repclie^ 
itur  punAum  A »  &  repulfum  prxcedcff^  SX 
'pundum  B  (iibducatur  punAo  A  »  attrahetuc 
idem  A^  ficque  attraAum  (equetur. 

CoroU.  Hinc  itcrum  patct,  cur  Utnitcs  aUqm  H^ta 
audiai|t  cohafienis. 

SVL  SffunSu  in  lisfiHlbus  mn  eobafiouis  fim 
tumttur^fieiiautttfm  teteum  ufpgner  verfus  dtemph 

P  4  Ir^ 


^ 


i9  ScSlhl  Gfmm. 

^onu  scee^Unt ;  H  Mherum  tk  sltiro  fijH^niir^  Jh^ 
U  riceJita.  demonftrationem  vide  Theore« 
mare  ;• 

VIII*  ^punSum  vi  ixigua  JimcviMur  slimi^ 
ff  c^hafiomSf.  redfbit  ad  limitem  eum  modica  ofeiBs^ 
tM«#»  Tcu  hinc »  &  illinc  procurfione ;  facilc 
#nini  per  vim  conrrariami  in  quam  incurrir^ 
niinuecur»8e  exftinguecur  modica  illa  Yclociraf 
pimifto  imprefTa. 

Sth^L  Sic  neque  elaftram  leniter  comprellam » tut 
liidudum  muituro  o(ci1Ut. 

'  IX.  Si  punSlum  vi  exigus  dimovestur  s  li^ 
ndte  nan  cohajionis, )  magns  babehitur  ofiitlatio  ; 
defererur   enim    pun^um    ad   arcam  ,    in 

quo  vires  emfbirahunt  cum  direSione  PunSli  fea 
sccedentis^  (eu  reeedentis^  ultraque  proximum  co- 
hasfionis  timirem  procurret,  ^6  tum  primo  ha- 
bebitur  moru^rerardAfio,dein  celeritatis  prio? 
iris  elifio,  dentque  ^itari«« 

CoroU.  Hine  itttVLtay  fi  fuuRum  a  limite  nmcoh^ 
Jknk  m  ^anutHCHuquetuigua  dimomm  farvenias  ad  «r. 
€um  frouimun  hmie  oimphun^  habori  f^erit  iugms  oJUL 
heio ;,  fieri  enim  pa«erir,at  plurimi  iioutes  transcurrtnriia^ 
datli  4e«enktar  ad  arcam  cxAinguendaK  efluii  velodtad 

Eremy^ua  cxilinfla  redibit  pundum,  &  bocampHue  ojiilm 
lufr,f  fio  vafiiorfmrit  areus  froximus  limiti  uon  cobaJ$6itie% 

X.  Si  punBum  ali^d  confUtuatur  extrs  limL 
fti  I  sccedet  sd  sherum ,  vel  recedet  sA  iUo  (  prout 
fuerit  fiib  arcu  attrahentei  vel  repellente  coii-^ 
llttuturo  )  feraurque  ufque  sd  proximum  timitem 
^it/hms,  argtfue  &ilicet  ▼!  #itraafva|  aut  re- 


hf9kti\  qtiia  T«locica$  in  limiiibw  Mii  er« 
fitnguitar,  UA  tncipit  minui  firopeer  excipien* 
tem  vim  contraf iam ;  quare  imminma  cooti- 
nenter  relocitate  progredietar,  donec  fub  ar- 
cu  (equente  conficiar  fpatium  =:  priori»  (jnod 
arcus  prior  ab  initio  motus.  ufqtie  ad  limitem 
comprebendit.  Ibi  prior  veiocitas  omnis  ex« 
flinguetur.  Tum  vtro  puniium  t^Qct  curfum  ^  ^ 
Vf gente  iterum  vi  Cea  •nradiyai  (eii  repuliiraj^ 
if  ciris  timitem  c§bafkmf  tsmdhi  cfcilkkn  htnc, 
&  ilHnc  procurrendo,  dum  tiribtts  afiorum 
puhAorum  tmpediatur. 

Sib^h  I.  ConflitaatQr  pundum  ilterum  in  j^,  at- 
teram  in  z  fub  areq  repellente  LMN  ;  repelletar  nf^ 
^oe  ad  proxiinum  cohefioni^  limitem  N^  fereturqujs 
jceleritntt  aeqqifita  ^  tzN.  Noh  tamen  confidet  in 
limite  jllo  N^  quia  (^eleritas  acqinfita  fub  arcu  zfN 
nondum  rxftinihi  eftt  Transvolabir  itaqne  limitem  N^ 
fereturque  celeritate  femper  retardati  prppter  contra- 
riam  vim  attnhencem  uioue  in  n  ,  ubi  ne^mpe  N  yu 
*«'  ztN.  Tum  regKedietur  in  N  motii  accelento » 
iterumque  in  %  motu  retardato.  Hiiic  denoo  riam  re« 
leget  in  u ,  denaoouc  iii  z,  Sic  iret,  ac  rediret  in  infi« 
«liftm,  ai£  a  xwm  mrtnca  metua  lA»  alternii  accele« 
Mtut|  ae  ratardatm  fiibiiide  fiAerttur*  idan  evevitee  ^ 
fi  pandum  tikeroitt  aen  yam  io  « »  (ed  In  a»  looibitiir  ; 
mm  qula  fii|)  arca  aisradir«  conf^tuetur,  transgrcdit- 
tur  limitein  JV,  procnrretque  in  z ;  ibidem  re^redietor 
in  u  Gtc.  Do£lrina  hxc  omnis  egregie^  illuftratur  per 
chalybemn  elafftoin, 

4 

SchiU  It.  Adhuc  qacpiam  adnotabo*  L  DiSa 
€jiiJIa$io  hcufn  mn  babit  ^  fi  puu9um  ultra  cobafiomt  tf» 
fmtcm  fncurretif^  tf  aream  priiri  ss  tmficitiis  ai  ft* 
mitem  alium  qunmunfne  ckfcranir.    lfto4  wm  fi  fiat^ 


^  I 


90  S$Si9*t  tkfut  Ilt 

tJiqtxc  aret,  ^Qftm  trcus  ab  mi rio  motns  MlqQe  ti  praiti-  - 
mum  cobiifi&nk  Itmitemeomprebendic,  iic  s  coti  arec 
ftrcuf  (tqoentii,  q«te{cit  (^. prcCTbeor.  i.  > ,  cum  niil- 
lis  ibi  viribus  urgeatur ,  &  omnis  pii^ior  rclocitas  pec 
exeipientcm  vim  comrariam  exftindla  iit.  II.  Si  area ,, 
fuam  arcm  frhr  ab  ihith  motus  u/que  ad  proximum 
coiajtonif  limiHm  comprebefidit ,  ^  efi  fubfeqttinu , 
futtSum  trattsvolabit  proximam  Htnitem  tiott  cobaifionu  ^ 
cum  in  eo  prior  veloeitas  nondum  exfliinda  ponamr* 
jftque  fofiea^  cum  ingrediator  aream ,  tn  qua  invenit  ti* 
res  cum  oiotQ  fuo  conibiraotes ,  feretur  motu  accekraso 
ad  Ihttiwn  alittm  ^bggfiQttiSy  quem  itertm  pratergrediettt 
ftretnr  motu  retardato ,  &*  (iq  deiftaps»  Ifla  tnoftts  acce» 
liratij  ae  retardati  vicijjitudo  babtbitur  eotijque^  dum  puti" 
Sum  deferatur  adarcum  toti  velocitasi  Jita  ex/iiftgtiend^ 
parem.  Ingens  bsc  agitatio  cum  ofcillationibus  varii^ 
&  motibus  jam  aecekriitis ,  jam  retardatis ,  jam  reflexi& 
fervit  ad  e!lcplicandas  fermeutatioues ,  &*  deflagratioues» 
III.  Si  area  priQt^^  efl  c^nfeqltente ,  piinBum  nou  eme'^ 
tietur  totam  aream  feqttentem^fed  ubi  aqualitas  arearuna 
mrittque  obtenta  fuerit  ^  contittuo  refle^t  curfum  \  nana 
obtenta  arearum  atqualitate  elidetur  veiocitas  (ub  priore 
areu  acquifita ,  punaamqui  argcbitur  viribus  icu  attra« 
aivis,  fivc  re^ulfivis*  .  ^ 

XI.  Si  jntHBs  du$  iH  Utmi&us  taistjkftts  um^ 
fiima  pfvjiciantur  Miqui  motiiut  n^ntrmis ,  if  sf» 
aualibur^  ita,  uttmboratA  direAiones  cum  rt&u 
jungente  ilU  duo  punAa  efficiant  angulos  :=:^ 
&  admodum  parvos  |  punSum  tjus  rtBd  jungtttm 
tis  medium  manthtt  immotum ;  ipfa  auUm  dtto  fun^ 
Ba  circa  id  punSum  gyrabunt  in  curvis  lintis  ptatt$ 
Jimitibuj^  &  aqualibus,  Theorema  hoc  stfani 
prf  (Iai:  in  e^plicandis  mct^dkrum  Ufniien&uH 


SdM.  t  Qyat  hiaen&f  dida  Cmt,  fcre  p^ttncnt  «1 
pnnfia  duo  fikimct  reli^la ,  6c  fuif  duntax^  viritm  •• 
gentia  pr6  ratione  diftanttj^rum.  Si  vif  extmm  acc$^ 
dtty  foteruttt  pun&4  ntom  etiam  Mcehrato  0d  lii^tem 
'tohffimis  delMjiflij  quo  cafa  nulla  habebitur  ultni  li- 
mites  transcuriiOy  nec  oftiiiatio,  cum  in  limitibua  prlor 
Velocitas  omnia  a  vi  extranca  exftingui  ponatur.  IL 
fotermt  vi  extema  comfrimiy  fit^  comfrejfa  dtutiuc 
retifseri  fub  arcubus  valiMffime  repeUeutibus.  Item ,  f^ 
teruut  vi,e(tdem  eaftenta  a  fe  fe  diftraii  ,  E^  di/ttad0 
diutiut  retifteri  fttb  arcubut  validiffittie  attrabemibm  y  fie 
tamen,  ut  ceflantc  vi  oKtema  nitantur  €c  in  poGtion<fi| 
priftinam  reftituerc  inftar  elaftri,  aut  quorumvis  alioruoi 
corporum  elafticorum,  in  qttibus  arcus  vicini  iimitibuB 
cohseiionis  (unt  egregie  ampli.  III.  poterum  funSa  ^ 
iagente  vi  extranea  fic  comprimi,  aut  didud,  ut  in  mayort^ 
efictuitme^  aut  diflautiA  ^antter  %  Jmtpe  fimfer  in  limi* 
tibm  cohstfianis  ;  quoil  accidit  corpofibDS  moUibus  »  ia 
^uibus  magna^habecur  limitoai  frcqncntia^  nequc  jvicioi 
•rcus  (imt  adeo  ampli, 

ScboL  11.  Ex  omnibttS  iis ,  qu«  a  {$.  3««  ad  hutQ 
nique  locum  Congeili ,  abunde  iiquet  :  magtiam  vel  in« 
ter  duo  punfla  diverfimode  locata  efle  virium,  &  a£tio« 
num  varietatem  ;  (emper  tamen  ii^  diftantiis  adlwc  txi* 
nimis,  quattsm  Bg^  s.  exhibemur  abw^  ufque  in  Jt, 
nbi  curva  pet  variaa  ambages,  leu  ftaxtiofbs  anfra£l«f 
dufta  fiepe  circa^axem  contorquetur  ;•.  nam  ot  primuia 
punda  ultra  JR  delata  foerint  ad  majores  diftantias  c.  6f 
jfl  0,  vel  u,  nalk  habtbitur  aQionum  varietas ,  (ed  folio 
mtrafHo ;  cros  enim  Tjp  s  V  pertinens  ad  (btas  diftait* 
,tias  mafor^  totum  jacet  infra  axe«;  quarcoxbibet  v!» . 
ffcs  duntaxat  attrahentcs*  Jsm  «  pon£Us  doeboa  a4 
tria  gradum  fiicio  ;,  patebit  maforem  adhoc  virimi  aonu 
pofitionem.,  motiininque.&  aSionum.diverfitatem  eni^ 
fd  debci^  fcA  iii  diftaiicUi  uccim  msms^ 


_/ 


f 


v^.  f7«  Ad  hitelligendiim  r^ftfttlt  ffiam 
pimAorum  facient  tria  cumprtmift  problMiii* 
ta*  I.  Sf  ifia  funSU  A^  i),  B^  (  Fig.  3. )  /w/wi 
f^  $»dtff  reSla ,  ditermimr$  vires  ,  IjT  Jircaiotut  > 
^M^tf/  medium  punflum  D  a  binis  alsis  A(f  B  ur^ 

inftar  •bfciSarum  in  pun^um  A  Ffg.  im»; 
^«(inent  vel  amka  (ub  arcu  MtraQiva  1  vd  mn 
JFir  fab  npuljbsa^  vel  deniqtie  tf/i#rii  /«i^  mtrn^u 
V9 ,  #/i^4f  fids  r^fulfiva  ;  tibkunque  definant^ 
liotentur  ordinatje  geminis  abrcillis  refpon« 
clentes,  Sique  ordinat£  amhs  termin^intur  iil 
^rcu  attKaSiivo ,  aut  amba  in  repulfivo ,  advertera 
^portet ;  aqualtsna  fint,  an  inaquaks.  Sidqui^ 
j^i  ;  mancbit  pun^um  Z>  immotum  ;  tafitun^ 
dem  entm  tranetuf  ,  ant  ropelletpr  pairdttm 
JP^th  A^  qoamum  ai  &  Sunt  vero  dire^io- 
iiei  pun^orum  A  ^  Sc  B  tertfum  aliquod  ma« 
dium.p<in<f)um  D  trahentium,  aur  repollen* 
tium  e  diametro  oppoUtx ,  &  (per  bypotk)  «« 
qdales ;  quare  vis  pun^i  ^f  (einper  elidetur  a 
vi  pondi  B  (%3*  CtrcU^  Uh ) ;  proinde.  Si 
hue^uahs  fuiu :  movebitur  ponAum  D  (ecttn* 
dum  direAmtem  ponAi  fortiorts,  &  movebi« 
tur  >  tinqnamii  urgeretur  fbFa  differenfia  vi- 
rium  (  5-  J-  C<^^^*  (^*  )>  ft«ni  pars  aliqua  vt- 
rtum  a  pufi^o  fortiore  impeodi  debet  ad  olU 
dendam  vini  contranam»  minusquo  fortem» 
Si  deniqtte  ordinataram  m%a  tefrfmnetar  in  «r« 
Ctt  aiUfo^ta ,  aktra  m  npvifiuo ,  confpiri^uitt 
Viro»  y  9l  AreAf#fi€s  pun^  timttsque ;  quare 
pundlum  0  eecfeda:  td  pmtAtmf  i<  <  il  puo- 

^um  4  «ctraherc  ponaturi  &  B  rcpellerej[ 

vi 


tix  virium^  9  J 

Ti  coinpbfit^  utriusque  pun&i  4^  6t  B^  h.  t^ 
yi  a^quali  fumnus  virium  if,  &  £• 

IL  Si  tria  puH^M  A^C^B  (Fig.  IV. )  mn 
jdeidnt  ifi  4ir$^um  i  MurniinAr^  vir$s  ^  Vf  dU 
rtStxomi  y  quihus  pun&um ,  C  urgaur  m  htntf 
tUis  J,  ic  B.  R«  pmdtkAyC,  B  juDgantur 
teftis  AC^  BCj  AB^  completoqae  {^XoACB 
bifiriam  fccemr  linea  ABinD.  Ex  puodo 
WkStuirtn  D  ducatur  reAa  in  C ;  (Tico :  do^ka 
Z)  C  perpendicuUris  erit  zdAB^  &  angulos 
in  vertice  C  bifecabitur,  fi*if  C  ^  JSC  (  do* 
fBonftratum  enim  habenc  Geomerrie  :  Ji  in 
jJl^U  ssqmeruro  f  AuBs  ^ufiAm  nBa  tx  -anguh 
p:  lAus  laitribus  imsrupto ,  %& ,  (eu  lacua  angOik 
lo  illi  oppofitUTO  feMurb^4srism  ^  ficssri  adangn* 
hi  riOis  »  proiocifque  lineam  biifecanteni  eflo 
perpendicularem  ,  if  angulum  isi  wtiie  iiisUn^ 
/ccari  bifmam  ) .  Porro :  fi  iJC  =:  BC^  circino 
intcrcepta  earuiti  una  applicetur  axi  curvac; 
virium  ,  debet  (  ex  hypothefi  ^equalicatis  ) 
fiye  £ub  ^cu  attra^livo,  five  fub  repulfivo 
eadem  ordinata  rerpondere  utrique  ab/ciflk;' 
Icerum  ordinara  transferatur  in  Figuram^tam  | 
fiquein  arca.4rcraW/  cermioatafuic,  transfe- 
retur  yerfus  A^^B%*c.\nUicK\  fi  in  nptU 
kntif  deferatur  ad  partes  oppofitas  in  M,  &  ^* 
Utroque  cafu  compleantur  parallelogramma 
LKf&Mlf.  Cafu  primo  pun^um  Cviribus 
attraAivis  CL,  &cA  incitatum  defcribet  dia» 
gonalem  CJF.  Cafu  altero  idem  pundum  vi- 
ribus  repuUivii  C  M,  8c  C  N  impulfiim  pro« 
onrre^pef  reAam  CH^  ntad mltoitm  de mo>« 
tu  compofito  dicam* 


Cor^U.  L  Crgo  ptinQam  viribos  eJQtdcm  geiuxlt, 
&  cqaftlibiis  incitatDtn  ,  non  declinac  ad  Utat  aUam  , 
qait  poiita  attra£lione  diagonalis  C  F  congrait  cant 
perpcndicalari  CD',  pofitaqae  repaUioftf  CH  jacet  ia 
iirtSttin^  cam  eadem  linca  CD  ,  q«od  facik  dcmofi» 
firari  poteft. 

St  ACnoh  fit  =;  BC,  transferanfac  ambas 
id  axem  curvx ,  &  ardin^itjB  ii^  re(pondentes 
affidtto  notentur  in  f\g.  ^ta  (enrata  utriusqutf 
diredione.  Sint  jam  sna^ualii  mnb^t^  &  diverfk 
fpecUi^  five :  fit  vis  pundi  A  attrahens  e.  c.  CI» 
pundi  B  repellens  C  Af ;  iut  ex  ad ver(b  :  vis 
pundi  A  repellens  e.c.  CN^  punAi  B  attra* 
liens  CK.  Completts  parallelo|[rammis  LM^ 
vel  /Cjfabibit  punAum  C  per  diagonales  C/« 
vel  CG.  Sint  ejusdim  fpiciri  stnha^  fed  inaqM* 
ics^  defcribetur  diagonalis^  qusnoo  jacebit  ia 
tadem  re^a  cum  CD^ 

CortSl.  IL  £rgo  panfiam  incqaaltbat  viribnt  im. 
pairatn  dcclinabit  ad  latat  alteratram^  9c  pro  varietate 
iiidtqualitatum  varie  declinabit. 

Scb0L  Vls  ad  latera  impellent  CJ,  vel  CG  prx- 
elarum  in  explicanda  malTaratn  rigiditate  adferre  (biet 
adjumentum»  » 

IIL  ^j  punBa  Juo  A^  fSt  B  fta  ftH  in  hinif 
tjusdcfn  iUipfios  fvcitp  if  tcrttum  umunque  in  qus* 
dcm  pcHphcria  e.  c.  in  E^  vel  0»  vel  C,  dctcrminm 
virci^  (f  d&cSioncsj  ^uibus  funBum  C  urgitur  s 
duohui  iUis  A^  Cf  B. 

SehiU  Ptaca  noubo  prios ,  qoam  problemati  btiie 
fititfaciam.  I.  Si  i  bism  ficif  Md  idem  perimari  futh 
Bum  4uc0Hfur  dsuc  nBcCf  crit  iniUi^ iMr§mfumma  at 

axi 


Lnevtrium*  95 

'  Mxi  tnmfvirfp^  h.  c.  majoru  .Qviare  ( t»  1%.  5>  )  -^  B 
^BExA  F0$  Siqut ad // ducercntur  ttOx yiH,  Qc 
BH ,  ficrct  itcrnin  y1H+  BH^  FO.  Ex  eadcm 
ratione  AC^BC^s  FO.  II.  5»^£  sa  BS,  crit 
y^E,  vcVB£=3  dimUiato  a^xi  trafjjvtrfi,  fire :  ^£^ 
vcl  B  E  =3  f  A  aut  0'D.  III.  Si  -*  C J>  5  C,  /^^» 
tuudi^  A  C  txadit  fnm  axem  tnajortm  ,  quMmum 
BC  at  fodem  dtficu%  {SiDgok  barv  thtoireinatt  fimt 
Gcomctnf  notiflifna. 

His  pbfitis  R.  QiSQCttnqae  perlpheric 
loco  confiftat  panAum  tertiutn»  ducantur  linea» 
ttAsi  exA^ScBy  tria  hzc  punAa  jangentes; 
iterafnque  appltcentur  axi  carvac  yirium.  Sie 
Xroo  pundum  hoc  tertium  in  E  vel  H  loca« 
tam  »  fitque  ij  £  s:^  abfciflae  A  NFtp  2da  ex* 
hibitae :  nulla  lineis  noftris  A£^  &  Bi^refpon^ 
debit  ordinata  ;  quiefca  i^tur  futtShm.  2da 
fmMur  in  O^  velF^  quiefejn  ittrum  ;  ducantar 
enim  ex  punAis  A^  8c  £  lineat  if  0"^  8e  JB  0>  qua* 
rum  fiimma  =:  FO  r;  2DO {pcr  Tkor.  I. ProbU 
frdf)\  tantundem  if  0  excedet  femi  axem 
tranKverfuni  D  O^  quantum  BO  abeodem  de« 
ficief( ^rH&ror.  J//.)  . .  Deii^de  ponitur  D  0 
s  ilfs:  if  2«7  Fig.  2d« ;  quare  ficJ  Olimitem 
cohatfionis  H  excedet»  ficut  B  0  ab  eodem  de- 
ficiet  ;  proindeque  fi  linea  A  0  translata  ad 
axem  curyx  pervenerit  in  u,  definet  BOinz^ 
&  abfctffis  Az^  A  u  fub  diverfis^  ied  dequalibuf 
arcubus  refpondebunt  asquales  ordinatae.  1 2r» 
y  ff ;  quare  tanta  erit  attraftio  pundi  if,  quan- 
ca  repalfio  punAi  B  ;  4tbit  igitur  punBum  in  0 
hcsium  memm  immtum.    loem  #kttnet  circa 

pUAP 


^^  pundum  F.  gtio  :  Si  punBmm  ^uHunqm  sU» 
pcrbnitri  loco  confiituttur ,  t.  c.  in  C,  nHetur  ukiru 
f€r  tMgcnUm  P  ^  Nempe  :  congruat  A  C 
cum  Au  Fig^.  2, ;  &  £Ccum  Az^  notentur 
iftts  rerpondentes  ordinatas  in  Fig.  5. ;  exhi- 
bebit  C  L  ordinatam  uy^  6c  C  M  ordinatam 
I  z  ;  completo  pafallelogrammo  L  M  iotbit 
pun Aum  C  viam  mediam  ^  procurretqiie  per 
diagonalem  C/,  qux  pars  eft  tangentis  P  O^ 

'  Idem  in  aliis  quibusounque  perimetri  pundtis 
ovenire  neceflum  eft.  ^to :  Si  punSum  C  Ji^ 
movcMtur  di  ptrtpietro  ellipjfios  FHOE,  continuo 
fti  rcUHum  sd.  oandcm  regrcdUtur^  Verfetur  e« 
nim  uttra  perimetrumi  erunt  AC^^BC  majo^ 
Tt%^  c|uam  fi  in  perimetro  definerent;  verfe- 
tuf  citra  perimetrum ,  erunt  AC  ScBC  mino« 
resiquam  fi  in  eadem^  perlpberia  termina** 
rentiir,  Quare  fi  ad  axem  curvas  transferen* 
tur :  if  C  imocafu  magis  recedet  a  limitpcobzip 
fionts  Ni  &BCmagis  ad  illum  accedet»  quam 
ante ;  proiodeque  completo  parallelogrammo 
puodum  percurret  diagonalem  a  tangente  di« 
vergentem  doorfum  ad  perimetrum.  Altero 
cafii  BC  magis  recedet  a  limite  cohatfionis^ 
,  quam  ante ,  SicAC  magis^  iccedeti  h,  e«  major 
habebitor  repuUio  pundiA»  quam  pundi  A^ 

3uare  pun^um  C  abibit  per  diagonalem  ten* 
entem  fiirfiim  ad  perimetrum  priorem.  V^ 
trobique  pundum  regredietur  ad  periphe- 
riam,  e  qua  dimotum  fuit.  Sed  hxc  obtine» 
bunt  folummodoy  fi  panAnm  Cconfiftens  ia 
perimetro  cUipicos  »  fimulqoe  timit^us  cob^om 

fionif 


Lix  virium  57 

/!b»f/ ^iinoveatur  ultra,  vel  citra  peripbenanid 
FiM  pg.  6«  n.  I  •  Nam  5  to :  SipunHum  C,  conftitutum 
€9  perimgtri  loco,  quifimulSt  lima  non  cohajionis^  du 
moviMur  di  pcriphcria^  cominuofibi  rcUSlum  magis  sA 
taJcm  r€€€diti  nam  fi  ultrapcripbiriam  dimovebi- 
tur,erunt  AC,icB Cmajores, quam  forent  irt  pe« 
ripher»  termi hatx ;  fi  citra  pcriphcrim  ^  mino« 
reserunt;  zdeoque  uhrs  pcriphcriam  major  erit 
▼is  repuIGva  pundi^,  oeminorvis  attraAiva 
pun&i  jB  ;  quibus  in  Fig.  6.  n.  2.  debite  notatis, 
completoque  parallelogrammo  L  M  procurret 
C  pler  d^gonalem  C  I  furfiim  verfus  tenden^ 
tem ;  ^irii  pcriphcrim  major  erit  vis  attra^ftiva 
punAiif,  6c  minor  vis  repuKiva  punifti  B^ 
quibus  denuo  esdcm  Bg.  6ta  notatts  y  comple- 
toqae  paralielogrammo  LM,  abibic  C  per  C  t 
deorfum  vergentem;  Ergo  fcmpcr  fibi  rcliSum 
wtMgis  a  pcriphcria  rcccdct» 

Scboh  T^lii  fcr^  eft  YiciffitQck)  inotfitini ,  ac  virium 
iatir  tria  funda.  Quid  jam  ,  (i  4,  $,  6^  &c.  imituo  in 
(e  (e  tganc  ?  Quid  (1  malTs  integtfli  innumeris  prope 
punSis  conftantes  ?  ar.  non  incredibilis  qnxdam  viriuoi 
flC  moti\ttm  varietas  confurget  ?  Confiirget  ftne  ;  (ed 
motui  ilH  omncs  utcun^ue  varii  ex  onica  lege  noftra 
velut  (ponte^Hia  proflu^ht ;  fcd  omnis  iila  VtriQm  com« 
poiitiOi  &aQionum  diverfitas  repercnda  eft  anufnerc, 
&*  iifiributiOHe  pun&orum  particuias  minimas  infenlihi* 
les  eonftituentium  ;  (ed  denique  motus  ilti  diverdflimi 
exnirgunt  dumaxat  in  minimii  diflantiis^  niim  in  majori» 
hushthtix\x^a&\o  unica,  (cilicet  atrra^iva.  yf  parvitatf 
dijiantiarum  pendet  tanra  virium  ,  ac  motuum  diiTimi!t« 
mdo  in  particjilarum  coh«(ione,  fermcntationihus,  odo. 
ribuSi  (aporibus  &c.  Ex  tnagnitudiue  diftantiamm  ratio 
filincnda  isft^  cur  gravitas  bmixittm  corporum  e.  c.  texw 

0  reftrium 


1 


9g  SeSHo  L  Csfut  IIL 

ftftriinn  proportionttii  fit  mtfljr,  iBquiin  tendont»  Qt 
j         jqntdrato  difttntic;  leu  i  cur  vis  illt,  qoc  motQm  corpp- 

rum  inflrqntiium  ex  xqutli  tltitudine  deltbentium  tcccw 

lertt  (  fubtnotii  wtptdimenti^  exumis  )  squalis  (ir.  Sitf 
'.  ouruini  &  plumult  ex  ctdem  tlcitudine  demiflt  ttdoip 

od  (eniiim  celerittte  deltbuntur  in  vmcm» 


^.  98*  Cfiff  J  buaifijH$  ixpofiiM  ixk^  I^ff^ 
iAriumi    Vr.  Vires  in  ulttmis  diftantiis  rtpuHU 
^^s^  ciiivts  velocirati  exftinguendte  pares »  im« 
minutis  in  infinitum  diftantiis  creicentts  iq 
iftfinitum  ,    auftisque   decre(c«ntes  exbibee 
irus prifnum  aJympMicwm  DgtEf  cum  fiiis  6rdU 
Datis;     Vires  evane(cen6es  figniBcantur  pon^ 
itis^  quae  IwiiM  dicimus.    Alternatto  vis  repiiU 
fivci  8c  attradivse  exprimitur  per  viciflitttdi*» 
netn  mriuum  fiipiHorum^&  infiriorum.    I^rpetua 
dlenique  attradio  agens  in  majoribos  diftimiis 
in  ratione  reciproca   dnplicata  diftantiarum 
per  ordinatas  a  crure  arymptotico  Tp,$V  du« 

&as  ad  axem  AC. 

\  »  • 

Scbih  At  inquies  :  Neque  inter  punfit  elemtntt** 
fit,  neque  inter  corpor^  dtntur  illi  axes^  urcm ,  ordini^' 
ta  ^c. ;  ergo  per  txes,  trcus,  ordint(ts  &c.  nequeunt 
fxplictri  corporum  proprietttcs ;  tcproinde  omnishffC 
curvt  videtur  efle  figmentum.  fj^.  Sicntmon  fphsrt 
tirmilltris  fignientum  eft^  fic  nequc  eurvt  nodrt.  Stns 
aon  dtntur  in  corporibus  ixes^  ircus^  ordinaia  &;c. ,  tt 
dtntnr  et»  qu^  per  axes^arcus,  &c«  defigntntur.  Sed 
Qeqne  ia  coelo  dtntur  Horizofi ,  Meridiauus  y  Xquator^ 
tlitque  ejosmodi  nott  Aftronomis  nomint  \  quis  ttmcn 
neget  reOe  et  felieiterque  tdhiberi  ?  Dices  11.  Qoi 
htnc  virium  legem  tnentur,  neqneunt  definire ,  qut  in 
d^nUa  sttrttlio  obtinctti  aet  rcf  uUio }  iteoi  quibus  iii 

difttn* 


y 


i 


.iKftintiisirrpiiUiom  (ucceclaf  iKraAio,  nt  TieiilHn  ;  erg^ 
tam  curva  illa,  qQam  lex  virium ,  cflvt  perpetuo  diftan* 
tiarum  meminit,  iitutiles  (unt.  l^.  Definiri  iflud  non 
poteft,  quia  neque  (endis  tam  acuti,  neque  inftrumentt 
adeo  cxa£b,  neque  mqdus  ullus  (tipperir,  ut  ptsn^a  (im- 
piicit^eorumqueabinvitem  dj(>antiasdetegere  poilinius. 
Sed  non  propterea  kiotiiis  eft  curva,  aut  lcx  virium;  (ecu« 
&  AfiroiHNiiiain »  qux  neqoe  nomerBm  (kellamm  fixa« 
rum  y  neque  difiantias  earondem  tum  inter(e,  tom  o 
Sbie  determinat ,  nequeaiia  exadt  deflnit,  fed  pitraquc 
duutdxat  ad  fenjtmy  inotiiem  efle  oportebit. 

ScboL  IL   Imtg;inef9  curvoe  virium  t  Neofono  pro^ 

{o(itx  exhibet  noftra  Figura  ^tia.  Non  piacet ,  quia  in 
ac  ordinttc  vtrlus  eandem  continuo.  plagam.d|rigun- 
tur,  proindeque  nulla  iiabetur  attra£tionam ,  ac  repul- 
fionum  (uccefno.  ado  t  qviia  perpetuo  ordinatjT  cre(cunc 
in  rationi  rtciprOct  dopiicttt  tb(H(farom ,  idecqoc  ^flC 
rircs ;  fuod  tamen  failcre  in  minimis  dtCiantiis  erai^ 
cnnt  oatorc  pharno^itt.  Ccrte  (i  imminotis  difttni» 
tiis  crefcit  tttrtdio  in  rtticne  duph'cttt ,  fortius  tttrtr 
hentur  moiecuic  corporis  denfioris,  qutm  minus  dend  ^ 
fortiusqut  cohasrebu^t  ptrticuls  auri^  quam  adamantis^ 


/^ 


Caput  IV. 


Applicatio  Legis  ad  pfjccipaas 

Corporum  propriecates. 

$.  ^9«  Proprietates  f  (ive  qualitates  ^  8C 
afiediones  corporum  alix  {iint  gtmrdts  ,  qusi 
corporibus  ooinibus  indmc  ^  alic  partiiulares » 
auas  in  omntbus  corporibus  non  experitnur* 
Ad  proprieuMs  getierales  Q^e&anc  filidiui  ^ 

Q  a  fivii 


*'•--: 


\ 


t06  &Si0  L  C$fut  tV^ 

five  impenetrabllitasy  exunfip,  ^UvifMitAt^  eobd^ 
nntis,  mobilitst,  incrtiSf  vis  attraSiiva  ^  &  gravitafm 
Ad  particulafe^ :  raritai^  denjitas^  &ex  ifs  nata 
Jivcrfa  gravitas  Jpecifica  ^  ntoUitics^  duritics  ^  fragi'» 
iitasf  duflilitas ,  glabritics,  afpcritas^  &  qux  ad  eam 
con(equitur/rf^ftf  ^  cJafticitas,  rcfiixio^  &cftuiji^ 
tas  y  ad  qiiam  revocabo  corpora  Uquida ,  tumi* 
da^  &  vifii>ja. 

&cboL  Sunt  qaidem  ali^  adhnt  corponitn  afTedio- 
xies  naturales,  w  lux^  calor^  frigus,  coloryfonus,  odor^ 
fapiditas  &c ,  de  ^uibut  tamen  opportunius  agetur  alibi^ 

§«  40.  Praster  naturales  iftas  «fFediones 
dantur  etiam  proprietates  quaedam  CheroicaPt 
iic  diAx^  quod  in  operationibus  Chemicorura 
per  miros  efFedus  fe  manifeftent.  Sunt  ex  z 
firmntatio »  foJutio ,  pracipitatio  ^  concrctio ,  &  li^ 
^atio.  De  fingulis  pauca  j  (ed  primum  da 
proprietatibus  corporum  naturalibus. 

Pf  oprictates  naturales. 

$.  ^l.  Inter  gcfnerales  proprietates  prU 
fhum  fibi  locum  vendicat /0/1^1/4/,  five  impem^ 
traMitas ,  in  qua  nonnulli  Phi^ofbphi  corpo- 
tutti  cflentiam  conftituunr.  Eft  vero  fblidttas 
4^a  corporis  afFeAio  y  ^ua  aJtcrum  de  Joco  fuo  ex-- 
aJuditUsit  ^^  nullis  natur^e  viribus  adigi  pof- 
fint  corpora  duo  ad  locum  eundem  fimul ,  ac 
iemel  occupandum. 

Schof.  t  Phyfica  hcc  &Uditaa  diflinguenda  eft  ab 
ilU  Machematica »  quam  Geoinetrc  in  fua  dimcnfione 
Vina  coA^ituunt «  &  omiujno  penctvabilem  cfie  fuppo* 
.v^:"  nunr, 


ics^ 


Iax  viriumm  tOt 

nunt ;  e.  c;.  eum  demonftrant  t  foUda  ino  pardDelifipedg 
inter  eadem  paraUela  phfia  conftituta  fffe  inter  fi  zz  lia% 
Liqact  aotem  gemin*  *iiU  parallelepipeda.  fe  fe  motao 
penetrere  debcre; 

ScboL  IL  Eidem  hxe  ftdidit4fi  Pbyfica  non  exda- 
4jt  penctrabilitatem  apparentem,  qxxx  habetur  ,  dom 
e«c.  oleom  pertranfit  marmor  doriflimom  ^  lux  vitra, 
•ot.gemmcs,  c^r  poros  corporom  &c*  Penetratiohxe 
vulgarifxtt,  non  vera, 

SchoL  IIL    Non  modo  ccf^^riina' ,  (cd  &  puuQfa 
flementariius  convenit  di£l:a  (bliditas.     Atqoe  ca  potif^ 
fimom  de  cao(a  nequit  ejfentia  eorporum  confiitui  in  impi" 
netrabilitate ;   elTcntia  cnim  convenire  debet  omm  ^  (Sc 
foli:       Adde ,  qood  etiam  fpiritos  impcnetrftbiles  eflTci  ^ 
live  corpos  4e  loco  foo  exciodere  poflbnt ;  fi  enim  matc« 
riam  de  loco  movere  valent,  cor  non  &  areere  ?      Deni« 
que  fi  eflfentia  corporom  fit  impenetrabilitas  ?  corport 
\  compenetrata  corpos  non  eront,  cum  elTentia  ad  omncm 
latiinme  ilatom  pertingat.     «^i  inquiunt  adverfarii :  non 
iihpenetrabilitac  aSualiSj  fcd  exigentia  impenetrJibilitt* 
tis,  qoam  alii  impenetrabilitatem  radicalem^  vcl  iu  aSu 
frirho  dicont,  eflentia  corporotn  eft,  qbx  (piritibus  nol« 
lis  convenir,  (ed  corporibos.     Reddam  ego  :  fed  aotcm 
Don  (blis  ;    nam  convenit  etiam  punSii  elementaribufd 
J^,  ddo  :v  Qoid  exigcntis  illios  nomine  veniat,  (atis  noit 
AiTeqdors  an  enim  defideriom  qooddam  inreUigunt,  se 
cupiditatem  9  Rideo*    An  coadionem  aliqoam  ,  ac  ne« 
ceifitatcm  DEO  inferendcm)  utlfle  Cnifi  pro  abfbloto 
dominio  fiio  agere  velit )  corpos  arceat  de  loco ,  quent 
corpos  aliod  jam  occopavit  ?  Abominor.    An  deniqoQ 
irim ,  ac  poteftatem  exciodendi  alteront  ?     Sed  vpQm 
hanc  vim  licet  eorporibos  fingolis  incfie  non.diffitccr9 
A)o  tamen  tsm  in  (piritos  cadere,  quam  in  punda  ck* 
mcntarla.     Alii  dicunt :  .cxigemia  h^e  figmcntom  ejft, 
tcrminos  inanit  cft,  coi  noUa  notio  f^efpondcry  pltnc  ficut 

§ff€Hm  tni^0rh  (U  m^s  fortnat  fub/ia^uihs^  mtt  hatz 

G  j  ?«  • 


i 


lOS  SiShh  dfmtlK 

fr  vacHu      Sed  hrc  non  ego ,  qui  mitiai  (crib«PO 


tmo. 


hiquimt  IL  In  eo  artribnto  ftaeuendi  eft  nacnrr 
corporum ,  e^  quo  proprietates  reliquie  deduci  poftunt* 
Pedacitur  autem  ex  (bltditate  eiuenfio,  inertia,  mobili- 
HiSy  cohsrentia»  divifibilitas  &e. ;  ergo.  Qt.  Oportet 
iimiil  id  genus  prardicatum  primum  in  corpore  conci* 
piatur ,  &  (bti  cbrpori  convenii^t.  Soliditas  ai^tem  pri« 
mum  przdicarum  non  e(t ;  derivatur  enim  ip(a  ex  ?i 
repuKiva  corporum.  Convenit  ^riam  pundis  clementa* 
ribus.  Quid?  quod  attributa  rcliqua  cx  ea  deduci 
haud  poflunt, 

f  •  4I.  Pun£la  cUmintdria »  tf  corp&rs  omnis 
naturahur  folida  junt » ac  impenetr^bilia.  Pr.  Ima 
P.  Punda  in  ultimis  di(l^nrii&  ita  (e  repellum» 
ut  iinn>inuti$  in  inHnitum  diftantiis  augeantuc 
Yires  repeltenres  in  tnfinicum  ,  (inrque  cuivfs 
Telocitati  exftinguendx  pares  (  $•  17.  i8«  AC 
19»)  ;  ergo  nunquam  penetrari  pofllint.  Pr« 
lldaPars/Si  non  punaa  ,  nec  corpora  fe  Cc 
tnutuo  penetrare  poflunt;  penetratio  enim 
corporum  fiert  deberet  fecundum  elementaj 
atqui ;  ergo,  Cicteruiii  iatis  corporom  {blfdita* 
tem  eyincit  quotidiana  experiencia  j  quodvia 
cnim  corpiis  aot  non  finit*  locum  fuQm  ab  aU 
lera  occupari»  aut  f)  refiftere  trequeat»  recedin 


SchL&ahimo  experientia  apra  eft  namraiem  cor- 
foram  feiiditatem  evincere.  Habita  nempe  experientia 
prtmom  arguimua ;  ergo  cum  nuila  vi  naturali  corpora 
aKligi  poffint ,  ut  Ct  {cin  rigore  pcnetrent ;  tam  cor- 
forufn,  qQam  ponflorom  vires  in  uitimii  diftantiis  fimt 


tex  viriu0U  10) 

y  43«  FsciU  filiditMs  expUcatur  ^e  turOMi 
In  hac  entm  habetar  crus  afytnpcoricam  D  ti 
(Fig.  2da) ;  quare  ordinatar  ht^  ag  8ec.  cre& 
cunt  in  ratione  inverfa  diflantiarum ,  ac  pro« 
inde  imminutis  in  infinitumdiltantfis  crefcunrc 
vira  upulfiva  in  infinitum  »  &  funt  cuivis  re^ 
locitati  exftinguendx  pares  ;  neque  alicer  ^ 
quam  infinita  virtute  DEI  fuperari  poflbnt; 
Hinc  fieri  nunquam  poteft»  ut  corpora»  naturi^ 
tiribus  relida,  vel  punAa  compenetrentan 

§•  44.  Extinfio  ea  corporum  affeAio  eft» 
jfiia  iocigunt  babere  partes  extrs  fe  pofitas ,  ra/^ef 
jaltem  judieiQ  fenfiium  emjunBas^  Juxta  alios  : 
afi  mukorum  extrs  fo  inviam  exiftsfaium,  co'fxifientUi 
inuno,  Sapervacaneuroi  credo^  agerem  >  fi 
corpora  omnia  excen(a  ei&i  demonftratum 
irem, 

Sclol,  bTatnrim  corporls  in  extenjtofte  litam  efle 
opinantur  Cartefiani,  qua  in  opinione  propugnanda  toii 
(iint*  MaU  ofinanmr  :  Si  enim  extenfio  m  corporia 
nacura,.  oportet  ex  ea  fluant  proprietates  corporom  oni« 
nes ,  ficut  ex  ttatora  /^li ,  iot  dreuli  fluunt  omttes  ha- 
rum  figurarum  prqprietaces  9  nh  Mrifeientroekm^  ado 
Oporrer,  primiim  ifC^prcAicatum»  Oportet  3110:  Coi}» 
veniar  /^«QKr  cor porieof .  Non  fluit  autem  t%  (bla  eit* 
tentione  var  inertite^vu  attradira^  filiditai^  moMitaefOLC» 
3do  :  Non  cft  priroum  prsdieanim  ;  quo  enim  jote 
primum  dicator  /  car-  non  (bLiditaa  prior«  }tio  1  Non 
iemper  convenit  eorpot ibui  -,  naiii  corpora  virtiite  £H« 
vina  compemtrata  adhuc  maaaiit  corpora  t  licat  noft 
€xten(a  -,  ergo.  Dices  t  Concepta  extenfioiie  conci« 
fttur  Gotpoft;  0190*  ^  Etiao»  oelieq^  gravitfte  CWB^ 
Cif  itur  corpus,  uki  non  natiira  corp orist 

P  4  §-4S. 


• 


to4  ^mthfUfutW. 

•  f  .  45:.    Extii^  f*eil»m  Mtt  txpUcMHm  iu 

tbeoru  nofira.  Sponte  enitn  fua  floit  ex  impe». 
netrabilitate  j  nam  fi  punaa  materix  ifi  mi- 
nimis  diftantiis  fe  repellunt,  necdfleeft,  fie 

J>unaam  extra  ptmaum , .  molecula  extra  mo- 
eculamj  ergo. 

^.46.  DiviJlhiUtai ,  feu  StmiHas  (  nota  ex 
termmis  itteaio)  eommunis  tft  emnibut  earperiiui, 
C?  aJmiranda  in  plurimit.  Componuntur  enim 
ex  rubtiliJfimis  maieriaiparticulis,  omnem  adeo 
-  captum  hominum  fiiperantibus  j  ergo  (S.  i, 
axiom«3.). 

Sabol.  I.   Adntirabilis  iila  particohram  corpora 

componennum  fijbtiltt»s  cx  pracit ,  qax  «dduco,  exem. 

ph^  ubertat  patebit.     Unicum  aari  grannm.tefte  fUJe. 

30,  tecari  poteft  in  1 0,000  partet  fitis  fpcOabilet.    Cum- 

^ue  unicam  auri  granum  cqaet  drciter  .     ,.  uniuf 

j.  . .      «../..  100,000 

digiti  <;ubici^  feqaituf  s   digitum  cubicum  auri  fecari 
^poflean  partes  aado  oculo  fitis  vifibiles  47,  619,  047. 

«i     "•    -^^fi*  yiudtlictrum  ex  ano  auri  grano  da.  . 
Oum  erat  fi  om  pedes  500  longum  c;  looo  poll.  (fingii. 
Ju  «lim  pedibus  tribuuntur  13  pollices ) .    fift  vcro  poU 
lcx  quUibet  diWfibUis  in  partes  600  vifibiles  .  quarum 
liiigul*  adaiquent  capillum  tenuiorem  huroannm ;  ergo  . 
«mcnm  aun  granum  duci  poteft  in  partcs  3,6oo,eoo. 

m.  Si  cupri  granam  anum  folmtnr  irt  fpiritu  falis 
«^mmoniaci,  &  orta  inde  Iblutio  admifceatur  »8554 
grantt  tf)n«,  eam  ccroleo  colore  tingeei    Pondat  aoten» 

Wnw  H«j«  gnoi  c^tMtor  -^ digiti^ici ;  qoarf 

10^000 

poi». 


Ltx  virhmi .  ^ 

^055,75t 
pon^us  grtnon3mtg5j4=3  — -— 'ss  105 

looeo  lOOOO 

Pollev  (at  (upra  dixi}  diftinguitur  in  partet  600  utciiii* 
^ue  vifibllcs  ;    ergo  pollex  cubicus  in  partet  600  ^ 
600^  600  =4  s  16,000,000;  proinde  cum  onico  cuprl 

'  .  575« 

(rflno  tirgantor  105  digtti  cubici  Hh— — *  (  C^A  fnfiioncm 

lOooo 

compendli  cau(4ncgtigam)tinguntur a£(a  is,<8ooooooo 

partcs  vifibiles.     Sique  ttngunrur,  necene  cll,  ut  fit  part 

«liqua  hujus  capri  in  iingulisiftia  1  a,6go, 000,000  parti* 

1>us  aqo<c ;  quarc  in  totidcm  ad  mtnimam,  divi(um  crat 

linuni  cupri  gyanum. 

IV.  Telte  Leuwnbo^kio  ^  fi  aqa«  immittator  grt* 
Dum  pipcris,  vtfiintur  in  ea  animaicula,  quorom  diame* 
tcr  fit  ad  diamctrum  gtani  Abuii  majoris,  ut  i  s  iooo# 
Po;io  animaicoia  figuram  (phsricam  induiflc.  Quia 
(^per  Mktbefim  )  fibara  fmt  in  ratione  triplieaea  diame» 
trcrtm  y  crir  amimaJculam  ad  granulom  (aboli  ot  1 1 
1000,000,000.  h.  e«  miile  miiliones  animalcoloram  ho« 
Tomcc  fibi  compofitorum  adcquant  volomea  grani  fii» 
buli  ma.oris.  Facile  iam  adducor,  ot  tiredam  »  qnod 
icripfit  Keillius  t  id  genus  animalcolorom  plora  miiiii 
fuper  aaculst  alfcujus  cuQ)idc  confifterCy  atqoc  commo« 
dc  rat:s  choreas  agere  polTe.  Sed  funt  animalcola  hatc 
orgi^  ica,  inftroda  venis,  fibris,  arteriis,  nervis,  moicolis» 
Vflfisquc  aliis,  per  qnz  fluunt  horoorcs.  Qnantim  ifto« 
r.m  cfie  oportet  lubtilitatcm  ! 

V,  Odor  corporom  (  qo^  fitoi  cfl  in  proflovfii 
qoibosdam  fidinis ,  &  fiUphureis  a  corpore  odortfWo 
profufis ,  &  ad  velltcandum  organom  (cnfbriom  rctpU 
rationc  dclatis)  facile  pcrcipitor  ad  fpatiom  5  ,  &  pltt« 
rcs  pcdes  longom,  quin  pondos  corporis  odorpftri  im- 
aninuator.  Diflfunduntor  itaque  proflovia  in  (phserasi, 
cojus  (emi  *-*  diamctcr  =&  5  pcdibos.  Forro  :  fi  iphc« 
ra  hcc  dividator  in  partcs  4tas  digitt  cobici ,  complc^ 

tor  wondon  ;  ^fijg^t  1 6.    Er^  fi  Ia  «oa  ^otf ta  ptir< 


\  - 


^g6  SeBib  L  Caput  IK 

ti  digici  cttbici  vel  unum  habetor  profiovia<;ny^enint  tn 
COtt  rphsra  effluvii  57,8^9;6i6.  Incredibile  autem  eft 
miicitm  hAtii  C  cum  efflnviA  tam  rart  vix  {enfaiii  affi» 
oere  poiTencl,  piura  igitur  haberi  dehent.  Scd  tamea 
pondos  corporif  odorif^^ri  (cnfibiiiter  aon  ihiaaitor* 

VI.  Adione  ignis  mire  dividuntur  CQrpora  :  Stur* 
ffnim  ittbdiifto  cakttio  comperit :  granttliiiQ  thoris  ^ri 

IJ 

^ntc  dtvitttm  efle  in  parres  750  ~  plurif.  Aqac  unk 
cia  una  vt  ignis  tn  ^olipila  refolvitur  in  vaporcs  ,  vd 
«xigoas  admodum  particulas  pluries,  qutm  fifqttentibtto 

notis  exprimantur  .•  153650  —  Unico  temporis  icnu 
pulo  fecuado  ex  bmpadis  eiljrchnio  phires  partieulflc  Itt» 

css  erumpunt,  quam  418660  — -*  (  coippeadii  caQ(a  fc» 

_        M,  5,  19f 
€1  "gnt  —  •—  ^-—      Indi^iom  boc  eft  t  in  primo  ctfii 

poft  nottm  5  :  poni  debere  1 3  Zeros.      \n  alrero  it^ 

ram  poft  %s  ^onmion  effe  Zeros  5.     In  tertio  poft  no^ 

<tm  6  ;  Zeros  39  )  .     Fa.mut,  dc  iux  ex  obviis  corpo» 

ribos  dimanant  dcaionftrant    moiecolarum  et  comp^ 

nentium  robtiUtatem ,   qast  concipi  vlx  p^fllt.     Stillt 

«lei  totum  conclave  replet  lamine.     Fumus  (  inprimit 

9  pa  y.  fulpbure  ,  reJiM  &c.  ortos  )  integrts  tdeo  plt» 

tets  perradit ,  ^  tngaftiflirats  qotsque  rtmas  permett. 

Scboh  IL  Sed  qoantaeiin^e  (it  corporom  {eSilittSydt 
torptticnlornm  ,et  componentiom  cxititts ,  non  tameu 
dOfpora  funt  dtvifibilia  in  infiiitum^  nt  volont  Keillim^ 
M^he^tbroektMt \  tiiiqtte.  Com  eaim  omata  corport 
{^erMeuipbyfiekm)  componantttr  ex  entibos  fimpliei» 
im  y  proptercaqoe  iudivijSfilibm ,  opot.  eft ,  eum  td  ei 
viribot  aoa  qotdem  natortlibat  (  quod  vix  fieri  poflft 
sAitrof  )  ftd  qoibtticttnqoe  tUis  dcventom  fuertt,  cefl«t 
«titf  ior  divifio»  ^cio,  trgonientttm  hoe  eitplodi  tb  Ad* 
^fiiiiiWti»fiDiplkittii0gtiioba»^  fi^tutf  tttteffi,qoi« 

cen* 


1 


Ltx  trfrM.       •  let 

ccnfent,  ^od  ex  inextenfis  neiittc|nam  fiert  poflit  ex- 
teafiimi  Sed  revocandi  iunt  ad  Metaphyficam^  Con- 
Cra  vero  adverfirios^propiignantes  divilibiiitatem  corpo* 
ram  ih  infimtQm,  miiitant  (eqt^encia :    "^    > 

I.  Omne  corpns  efl  finitam »  quare  non  poteft  eon* 
tlnare  partes  infinitas ,  cam  infinitum  neqaeat  contine- 
^i  in  eme  finito.  II.  Si  corpora  in  infinicum  divtdi 
^poflrunt  y  (equitur  :  magiiitudinem  minimam  «quarl 
maxims ,  «^nm  amb£&  centineant  infinitum ,  infinitum 
^ntem  non  fit  >*  unnm  altero.  UU  Vel  certe  fequi- 
tur  iafinitum  atiud  aiio  >-  efle ,  vel  <^ .  Sci»  it^ 
tum  ,  quid  refpondeatur.  Ajunt  1.  Ltcet  megnitiido 
infinita  non  poflit  contineri  in  magnitudine  finita ,  po« 
teft  tamen  nunaems  partium  infinicus  contineri  in  ma* 
gnitadine  finita.  IL  Non  (equittr ,  inquiimt  $  magnk 
tudinem  minimain  dequari  maxinMr,  cuni  non  repngnec 
kifinitum  alternm  airero  eflfe  >*  vei  <<  •  Mkm  fua 
-prbbant  ex  eoncepttbus  Matbematicia ,  c|iios*hic  loqi 
non  ftdducam  conftridos  pageliarum  brevitate*  Unum 
jftud  breviflime  innuo  ;  fi  magnitndo  finita  Matbemati- 
ce  concepta  compieflitur  infiuimm  ,  erit  illud  tnetti 
imagtnarium*  Mathetas  corpus  ipedant  duntaxat  Cvh 
trtna  dimenfione :  in  longum  ^  latum, ,  &  profundum« 
A  cctetis  qualitatibus  prflclcindunt^  Phyfici  non  iteiii, 
Sdo  deuiqii^  afflrmari  ^  mulrts  :  corpora  non  quideai 
«iiis  natorx  viribus  «da  divifibilia  eSls  in  infinitum^  {e4 
concipi  debere.  Frimum  dicam  ego  :  neque  virtute 
Divina  corpora  iiSivt  dividi  pofle  in  infinitum.  Neque 
iftud  dicendo,  derogo  Omnipotentic  DEI ;  iftius  enim 
tion  eft  facere ,  qux  contradiAionem  implicant  ;  im- 
pltcat  autem  partes  infinitas  contineri  in  ente  iinita. 
Aiterum  eft  c  quoil  conceptus  eum  finiti  div^ilis  tn 
infinitum  fit  mere  Matbcmatietui  ,  non  Phvficas.  Phjv 
(icus  advim  repulfivam  imminutis  in  innnitum  diflail* 
t&is  cre&entem  in  kifiaitumJaUaaquc  corporum  ^aiUitate|, 
ndvertere  (empsr  dcbet» 


/ 


1 

XOS  SeShl  CaputlK 

§•  47«  Col^^ff^ti^  9  ^u  Cobafio  $Jt  conjunSlio 
partium  pvt  aSualium ,  Jivi  poffihilium.  Con jun*' 
£t\o  partium  aftualiani  plerumque  dicitur  ^ 
biijlof  poflibiiium  unio  ;  fed  ucraque  genc^ 
rico  nomine  cohdfio  tvkA\t.  Adhafio  pertinec  ad 
partes  majora  ,  udio  ad  niinimas.  Cobafio  psr^ 
$ium  majorum  efl:  cGinjundio  earum  partium , 
quar  fenfuum  judicio  unum  exten(um  non  effi- 
ctunt*  .  C^bajfo  partium  minimarum  habetur^ 
dum  partes  cobaerentes  (enfuum  judicio  unum 
extetifum  efficiunt,  De  ultima  faoc  loco  agam, 

■ 

Sc/joL  xA£luaies  parte$  dicuntiir.Metaphy(ieis,  qiue 
yropriis  Cuis  terminia  continentQr»  Ttles  fiint  parte» 
borologiu  PojJiHles  ,  io  cfuibus  termini  pro  arbitri^ 
pofluQt  conftitui ,  ut  in  tafoula  marmorea ,  cujus  nuUa 
pars  re  ipfa  habet  ternlinos  citra  Hoflram  defignationem. 

^.48*  Cobafio  partium  minimarum  repetenJa 
tfi  a  locatione  partium ,  vcl  punBorum  iff  iis  limi'^ 
tihus  y  in  quibus »  auSta  difiantia  y  tranfitur.  a  re^ 
fulfiom  aa  attraUiotum ,  quos  ideo  Umites  cobs* 
poms  dicimus.  Pr.  In  €0  conftituonda  eft 
paftiura  cohasfio »  quo.  poiito  partes  refiftuiit 
tatn  fui  compreflioni  ^  quam  diftraAionx  ;  at« 
qdi  pofita  locatione  partium  in  lim^tibus  co* 
bxfionis  partes  refiftunt  tam  {ui  compreffionti 
quam  dittradioni ;  ergo«  M.  patet  ^  nam  in« 
tellefta  hac  refiftentia  intelligitur  cohatfio* 

m»  pr«  ex  $•  3  ^»  theor.  2.  &  4« 

..  .      ,  . 

CoroU*  Per  locai;iotiein  pirtittm  ih  limitibuf  eehs- 

fioflu  CKpU(MA4a  fimt  ^vam  piwDomna  cohaefionii, 


L$x  virium»  .  lO^ 

Explicat*  do  altqua :  1«  h/jpulfi  nm  fnnS^  editrtHU  inu 
peUitur  ^  alurum ,  quia  ii  pundam  unum  urgeatnr 
contra  altcrum ,  repelletur  illud  alterum  ,  repulfumquo 

!»rfl^Gedet ;  fi  (iibducatur  alrert,  attrahetur  alterum  il* 
ud,  &  attrafium  fequetur  (  §.  36«  theor*  6*  )•  IL 
Ccfpora  aUa  aliis  firtniora  fwft ,  feu  partes  aliquQruna 
£rmius  fibi  cohsrtnt ,  magisque  refiftunt  fui  compreC 
fioni ,  aut  divulfioni ,  qoia  partes  firmiorum  corporum 
fiatuuntur  in  ejusmodi  limittbus ,  in  quibus  curva  (ec«C 
axem  fert  perpeniiculariter ,  &  deinde  hngiwt  ab  eo 
recedit  (§'35*)»  111.  Sifpe partes  corporumdenfibmm 
Hon  aque  firmiter  eob^reut ,  ut  tninin  denfirum  ,  quo4 
videre  eft  in  auro ,  &  adamaiite  ;  quia  vis  limttum  co« 
hcQonis  npn  pendet  t  vit^initate  punttorum ,  (ed  ab  itt» 
fUuatiouey  ^  recejfu  areuum  (  ^.  j^.Coroil.  )  .  IV. 
Sape  rumpuutur^  aut  diffringuutur  corpora  ^  eoromquo 
moleculae ,  qux  prius  cohce^rant ,  urgente  vi  extrane« 
ft  le  (e  muruo  avelluntur,  quia  a  itmitibus  cohixfionis 
remota  abeunt  ad  limites  non  cohsfionis,  in  quibuf 
{iii  diftradioni  non  refiftunt  ($•  36.  theor.  V. ),  &«e 
quibus  dimota  ad  priorem  fitum  non  redeunt  (  f*  cit. 
theor.  III.  )•  V.  Quautumcuttque  corpora  fijfa y  aut  ru» 
fta^fibi  fuiinde  inierantur ,  priori  firmitate  non  coha*"^ 
rent ;  quia  eorondem  particular  aliquae  (  ese  potiflimumif 
qux  in  (liperficie  (cabra  corporis  rupti  prominem  )  ul« 
tra^limites  cohsfionis  progrelfc  deveniunt  ad  diftantiani 
yaiidifiimae  repulfionis  ^  ficqne  catteras  prohtbent  ad  pri- 
flinos  cohsfiphis  limites  reverti.  VI.  ^pflanata ,  ^ 
comprejfa  fiiperficies  utatnqtie  fibi  cobarent^.  quia  appla* 
natione  illa ,  &  compreHionc  acquiritur  infignis  multt- 
tttdo  Umitum  cohsfioais.  i 

€aron.If.    Inferes  i  Rcjicienda  trgo  eft  ftntcntit  , 
Ipicuri ,  &  Gaffendi  colisfionem  repetentium  a  corpum 
fiulie  hamatiSy  tmciuaWy  ^  quocimque  alio  modo  con* 
figutatist      IL  Rejicienda  eft  opinio  Cartefii  exiftiman* 
U$  cobcfionem  fium  cHe  iu  quietc  partium  ,  feu,  idio 

i«rtfa 


^ 


{Mrrefi  cohcfere  ,  qiH)d  juxti  fe  pofifs  qiiie(ctm  ;  binc 
Verq  /;/  fluidis  tninorem  ajebfft  efTe  cobdrfionem  ,  eniti 
f  partes  fiuiddrum  perpetao  quopitm  motu  inteftino  «gt*- 
fentor.  III.  Rejiciendus  eff  Purciotm,  &  rccenfiorct 
iK)nniilli>  putantes  cobaeiionem  pendere  n  fnunpo  p«fw 
#ilifi7i  contaitu  fecundnm  fupcrficies  planas,  &  «  frfffiom 
0«  al^  incambentis*  IV.  «lenique  rejiciendf  (iinf  Nrty^ 
mjianomm  tf/r^f/i,  docences  cobsfionem  repetendam .  ^ 
dTe  a  murua  partium  attra^one,  qu«  imminutis  di* 

ftantits  cre(ctt/<k  in  contaAu  immediato  fit  maxima. 

* 

RefeHimr  ofiifuo  L  fiam  tAmi  illi,  &  unci  partibuf 
«tique  fiiis  Conftabunt ,  iisque  mutno  fibt  cobareHtiim'» 
^Per  quid  vero  cokarthmu  ?  an  per  altos  iterum  liamof^ 
&  uncus  ?  t^ailtr  rebemtntcr,  nili  hoc  pado  tdmitti 
puteiti  procerTum  in  infinitum«  Noh  plscet  ^optfti^  IL 
tum  ex  quieu  partium  noh  intelHgatur  ptrtes  refifttrt 
fui  comprefjhni  ^  aut  avuijtotii ,  fed  diintaxat  tf^otui  /jy* 
cali ;  atqui  ex  eo ,  qnod  parficular  refiftant  mttui  loca« 
If ,  noii  imelitgitur  earundem  cobitfit  ;  ergo  ncc  eat 
quiete  partium.  Fr.  m.  Cohsfio  involvit  majorem  re* 
fiftentiam,  quam  qua  refiftitur  motui ;  tonge  enim  dif« 
iicilius  (eparantur  partes  e.  c.  marmorcir  fihi  cpharen* 
t0S  ,  tc  unita ,  qutm  contigua^  &  ttmmnta,  Cur  ve-i 
ro  ?  quia  fcilicet  particulsr  coh«renres  6c  units  refif^ftf 
not)  modo  momi  localiy  &i  &  di/ira3ioni;  aliicautefTi 
fbrnm  vi  inertix  refiftunt  motui ;  ergo.  Confirm,  Re- 
fiftentia ,  qoa  refiftitur  morui  locali ,  communis  eft  om* 
nibus  corporibus,  etiam  fibi  non  cohcrenribus ;  ergo  eit 
ta  ^ntelligi  ntquit  cobdtfio.  Fallit  opinio  IIL  Si  enim  c^ 
haifio  pendeat  a  mutuo  fuperficierum  piakarum  cofita8uyjjcr 
quid  tandem  6bi  cohsrcbunt  lincs  fuperficiem  compo* 
ttcnres  ?  per  quid  punfia  linearum  parres  ?  ido ;  oporrebi^ 
fiiperficies  quascunqat  <rf i^e /^vi^a/ity  todem  modocoh^- 
rere;  non  autem  cquf  cohxrjent,  quod  teftantur  cylindrt 
dno  marmereiy  aiiiqueduocii^r»#i  ( §•  i6.  SchoL  III.  Obj« 
^)i ergo.^  jib  aihrn  p^effiouc  cttMpfioiiem  non  ptndt» 

;t_  '  *  rt 


/ 


LexviriuniM  111 

re  eviQfiOi  eft  priRium  e  vacuo  BoyUano  \  tam  ixtvfi  btc 
C  minorc  preflioRC  aeris,  quam  fic  CjDhcfio ;  deniquc  cx 
«quaiireiiftcntia  agris  inrerni  communicantis  cum  cxtemo 
premenre^  qu«  fingula  fufius  dcduda  rcpcries  locojiipr.  ciu 
Errauf  Tk\  tleutonimiiorum  aliqui ,  qulbus  attra^io  a* 
gcns  in  rationc  rceiproca  dupllcata  diftantiarnm  caiila  eft 
cohaenonis;  ^iam  csiTdodrina  bac  manifcfte  (equicur  t 
majorcm  fcre  cohsfionem  in  (;orporibos  deniioribns  , 
^  quam  minqs  dcnfis  :  majorcm  iu  auro ,  quan»  iu  odB* 
tnante.        Fallic  confcqucns;   proinde  &   antecedeni. 

M, 
Prob.  Sequ,  M«  quia  D  sq  — «  nt  alibi  dicctur  ,  umi 

V      ■-        * 

iefifitates  in  ratione  compofita  ex  direAa  maffatum ,  flC 
invcrfii  voluminum ,  (cu  i  D :  d  =3  M  v  ;  m  V.  Jam 
fi  V  s  V  ,  cric  D: d  =:  M:  m.  Quare  quo  denfim  eft 
CorpuSy  hoc  plus  maffa  habeat,  eft  neceftc.  Major  mafla 
fub  eodcm  volumine  argbit  majorcm  vicinitatcin  parci- 
cularum  minimarnm»  aut  pundorom.  mpflam  confti* 
tncntiii^.  Major  vicinicas,  (eu  minor  diftantia  infert 
majoi^cm  attra6^toncm  ( in  horttm  quidem  fententta )  y 
majorquc  attradio  majorcm  cohcfioncm.  Aurum  igt» 
tur  firmiui  cobarere  dcberet ,  qnam  adamat^ 

Scbol.  1,  Moneo  itemm  ;  non  agi  hoc  loco  dc  ^o* 
hxfione  partium  majorum  y  quas  aliqnattJo  pcr  folam 
,  aMt  preffionem  y  aut  ^nrai»  cohstrcre  nunquam  dubi» 
fSivL  * 

Scbol.JSt  Oppofitiones  ad  jf.  48»  £^  Corott.  II.  per.. 
.  timntes.  Ima :  Nihil  cft  finc  ratione  fiifBcicntc  C  p^^ 
Metapi.  )  proindc  ncc  coh^fio.  Atqui  fi  cohacfio'rc« 
petcnda  cftec  a  locationc  pnn£lorum  iiT  limitibu&  co- 
hfltfionis,  haberetnr  cohsfio  fincrationc  fiifticienre;  cr* 
go.  Pr.  m.  cohxfio  haberctur  finc  viribus ;  vires  autent 
Uint  ratio  fuflficicns  tfrc£luum  quorumlibet;  crgo.  Pr# 
M.  in  boiitibus  ram  cohatfionis,  qnam  non  cohsfionii 
nulht  habentur  ordinatir^  proinde  ncjue  vires  ',  crg9» 


• 

.V 


N 


Iia  StStioL  CaputlFi 

tjt:  Ni  fabC  m.    Ad  Pr.  N.  M.    ad  hujus  Pr.  D.  A.  in 
limitibtts  millac  habcntur  vires,  habentur  nmen  in  di« 
ftantiis  atrinque  confequentibus  C.  A.  tici}ue  in  illis  ha« 
bentur  N.  A.  &  Cm.     Ratio  fuHiciens,  cur  pun£la,  aut 
particulx  minimx  corpora  conftitnentes  deiats  fucrinc 
ad  limites  cok«fionis  ,  erat  vis  five  attrahens ,  five  re- 
pellans  ,  prout  punfla  ,  vel  moleculs  Gtz  erant  (bb  ar- 
cu  attra£livo  y  yei  repuliivoi     Cur  porro  ad  limites  co- 
bscfionis  delats  fibi  coh^reant ,  illud  ratio  fufficiens  di- 
ci  debet ,   per   quod   reiiftunt  tam   (ui  compreCnoni  ^ 
€ttam  diftrs£lioni ;  atqui  per  locationem  in  diflis  limi« 
tibus  y  quos  immediatc  confequuntur  vires  hinc  attra- 
lUvc ,  illinc  repuifivx ,  refiftunt  tam  fui  compreflioni^ 
quam  avulfioni ;  ergo.     Dici  etiam  poteft  ;  punQai  vel 
porticulas  ad  limitem  cobafionis  jatn  uute  deUtns  in  iia 
perfeverare.,  ftatuinque  fuum  confervare  fer  vim  iiier^ 
sia ;   non   igitur  pergunt  coharrere  fine  vi ,  &  ratione 
fufficiente»     ^t  iiiquies  :  ergo  vis  inertiac  paula  eft  co- 
bsfioYiis^      1^«  N.  C.  vis  inertia?  fupgonit  locationent 
punftorum  in  limitibus  cohsfionis  ,  qua^  ip(a  locatiO 
caufiieft  ^ohsfionis. 

II,  Funfka  in  fimitibus  quibuscQnquie- locata  (  pro- 
iftde  ctiam  in  Umtibus  cobafiouis  )  quieftunt,  ut  diQnm 
(•  )6*  thcor.  I. ;  fed  per  qnietem  explicari  non  poteft 
cohslio;  ncquc  igitur  per  pofitionem,  pun£!orum  inlt« 
mitibus  coharfionis.  ^.  C  M.  D.  m.  per  qui^tcia 
omnino  independentem  a  virihus  ncquit  explicari  co« 
hcfio  C.  n%  dependeintcni  a  viribus  N.m.  ^Cm.  Di* 
ces  iterum :  Si  cohsrfio  cxpliccror  per  limitcs  cohsfio* 
fiis  ,  explicatur  per  quietem  independentem  a  viriius  ; 
in  limitibus  cnim  null^  funT  vires  ;  ergo.  l^.  IkA. 
iii  limitibus  nuWx  f\mt  vircs  ,  confequumur  tamen  iu 
diftantiis  mox  utrinque  vicinis  C  A.  non  confcquun* 
Uir  N.  A.  flcCm.  Aufla  paromper  diftantia,  yel  immi* 
niita ,  continuo  habentui:  vires  urgentes  punflam  ad 
ptiorem  ficum  reycni.  * 

•-         -  III. 


Iax  vMums  X13 

-III*  Si  pnnfta,  vd  ptmcolse  fibi  cohsrent  ideo, 
quU  delatc  runt  ad  limites  cohcfionis ,  poterunr  partes 
diffrafli  alicujus  corporis  hnt  politm ,  Jibiqut  intrita 
eadein  vi  cobsrere ,  qoa  prius  \  atqul  iftud  repugnaC 
cxpcrtentic  ;  ergo.  Pr.  Sequ*  M*  pdteruin  fuper^ciea 
corpofttm  roptorum  dcven^ire  ad  priores  cohxiionis  li- 
mitcs ;  crgo.  tjL*  N.  Sequ.  M.  ad  Pr.  N.  A.  utcun- 
que  polits  fint  corporum  quorundam  (uperficics ,  fem- 
per  tamen  prominenus ,  &  demiculi  habentur  nulla  ar- 
tc  pcnitus  abradendi ,  quod  in  fpeculis  etiam  politifiimia 
produnt  (eu  nUcrofct>fia ,  (eu  fmfc<t  per  ea  ,  fitu  verti- 
eali  ereda,  inambuiames.  Ip&  hs  partis  unius  promi» 
Ocnti«  fic  in  aftcrius  foveolas,  &  cavitates  fe  (t  intinuare 
neqneont »  ut  ad  didantias  minorcs,  ac  validiores  quos* 
piam  Itmitcs  deveniant ;  (ciiicet ;  prohibet  iftud  vis  re- 
peUens ,  quiC  (c  pun£Vis  quibusdam  prominentibus  ob« 
jiciendo  efficit,  ne  aUae  ad  fovcolas  po(fint  pcnecrarc. 

ly.  Licec  diftantia  intcr  (eparatas  fiifi ,  aut  rupti 
corporii^  partcs  augtatnr  ^  fibi  tamcn  intritse  pbterunc 
eobaercrc;  crgo.  Pr.  A.  Au&is  licet  didantiis  adhue 
haberi  poflTunt  limites  cohcfionis ,  cum  ex  lege  virium 
in  minoribus  diflantiis  per  vices  multas  habeatur  attra- 
fiionis  ,  ac  repulfionia  alternatio  (  §.  7t  &  2  a*  >  ;  crgo« 
WjL*  N.  A.  Ad  Pr*  D.  A.  Etiam  au£^a  diilantiaiiabcntuc 
limitcs  cobcfionia»  lcd  cafibus  nonhuliis  admodum  debi* 
lcs,  &  langttidi,  ac  prope  infenfibilcs  C.  A.  ^quc  for« 
tes,  ac  validi,  ot  prius  N.  A.  Sic  D.  Cs.  &  N.  Cm.  Se« 
paratae  ^orporum  partes  non  raro  adh^trent  magis,  mi- 
nusvc,  pro  rattone  Hmitum  cohaefionis ;  fieri  enim  poteft; 
uc  auda  diftanria  habcantur  jam  validiores  coha^fionia 
Umitcs,  jam  infirmiorcs ;  cum  robur  limitum  non  pen* 
dcat  a  vicinitate  pun£lorom ,  vcl  particularum ,  (ed  ab 
indinatienci  4c  rcQcfifu  arcuom* 

V.  Quantumvii  dues  iritcr  cjriindroa  (<|uoi$.i4. 
rcccnfui  }  febo  fufo  i^terjedo  ai^^f  tur  diftantia ;    fiU 


\ 
\ 


♦ 


114  SiBhL  QfuilK 

tamen  coTiarrent ;  miilroqQe  validios  cohsrent  i  qn^h  fi 
mmao  fibi  inrcninrnr  abfijuc  £ebo;  crgo>4a8a  diftantitt 
habentur  benc  validi  liinires  cohaeiionis*       ^*  ^  D.  A« 
Cohxrent  fibi ,  quia  diltantia  inter  paucas  cylindromtn 
partes  augetur  ,  fimulque  augetur  attradio  inter  partcs 
plurtma^  C«  A.  augetur  diftantia  inter  partcs  plupmas, 
ant  non  augetur  attradio  N.'  A.  &  Cm«    Primum  intcr* 
jcdio  (ebi  fufi  anget  diftantiam  intcr  paocas  cylindro- 
rum  partcs ;  adhibetur  cnim  ferc  cxplendis  duntaxat  ca^^ 
vitatibus  >  qus   in  (iiperficiebus  ctiam  politiflimis  rc- 
manent ,  quibus  expletis  pun£}a  duarum  fiipcrficiefuni 
longe  cquabilius  ad  casdcm  diftantias  dcferuntor.    Htnc 
^^c  diftantix  intcr  plurimas  fupcrficicrum  partcs  augcan* 
tur ,    utque  cavitates    accuratius    explcantur ,    febum 
fyfum  iuterjicitur ,   feu     calidum  ;    non    vero  frigi* 
,  jdom.      2do   Quantumvis  augcrentur  diflanriae ,  fimul 
tamen  at/gnur   vis   attroBiva  ;    nam   ipfie   adeo   (efai 
{particuls  caritfltes  ingrefls    trahnnt  cylindri  utriuf^ 
qnc  partes  ia  fiipcrficie  pofitas.         Dices  :  Etiam  aqu« 
cylindris  duobus  interjeda  cxplcntur  cavitares  ,  nec  ta* 
inen  fic  augctur  attradio,  ut  cylindri  arque  firmiter  eon* 
jungantur,  ac  hiterpofito  febo  ;    crgo  inane  refugiunt 
efl  in- cavitatibos  cxplctis.      ^.  1.  Nego  fuperficicruna 
c$|fFit^es  interjc&a  aqua  ad  amuffim  expleri;    fignra 
'^radlpolecularum  aquearum  minus  proportionata  cf!e 
vi(ietur  itnpiendis  accurate  cavitatibus  ;   hinc  marmori« 
bus,  autmetaliis  interjeda  minns  firmiter  ca  conjungir^ 
quamoleum;  planc  ficut  gluten  1  ignis  ife/i/Tori^itf ,  ftOt 
fiipcrficiebus  r^»r»far  iilitum  minorem  exerit.artraftio*^ 
ncm,quam  ichthyocolla.     j^.  II.  Si  libcralitcr  dem :  srqu^ 
expleri  cavitates  omnes  aqna  intcrjeda ,  tc  febo  fufb  i 
dtcam  ^fiien  msqualem  haberi  fiiperficierum  coninii* 
,<fi2onem'v^ptere«,  qood  aqua  minus  trahat,  quam  fi- 
Irum.     Iti  caufi  cft  varius  numerus,  fitus,  ac  diflributie 
luoleculArum,  five  pun6lorum  gemina  hsc  «orpora  con« 
iftituentium,a  qtw  nupieri',  ac  diftributioiujs  varictatc  va4 
uctas  pendct  atiraJtioDiSf 


/ 
i 


Lixtirmm*  115 

VL  Ntqmt  m  hac  theoria  cxpllcari  Imo  :  cur  aliA 
corpora  reddantQr  magis  cohxvcnxisi  Jrigere  ^  alia  iffn. 
Sic  frigore  in  inafTas  nrmas  a^ctint  vietaUa ,  refiut  trr» 
rtfirts^  vitra  pnus  th  igne  Hqociadla.  .  Fermm  iteoiy  ac 
tbalybs  ignittte  (ubito  in  frigidam  aquam  immini|S  indii- 
refeit*  Tel^  aratiearum  e  materia  fluida  contextde  ia 
«ere  con&itdantttr.  Igfds  ape  in  Jateres  firmiflimos  abic 
wolk  iuwm  i  otorum  aliumen ,  eajeus  item,  ac  treta  in* 
^^  dttrantor;  ^  Ildo  r  Cor  fluidgrum  aliqua  fibi  admixta 
cd^ant  in  madam  firmam»  Sic  tede  MufcbeiibrQeki^ 
ipirittts  conmcervizxkm  akoheile  vini  permixc^jSi  coit  iia 

^  ^nraai  maflani*     Albttinen  ovi  cnm  rpiritn  (alis  ^Drti 

ceminna  agitatione  firmiter  con«re(cit.  Oleuih  oUva* 
f um ,  &  aqua  fortis  foagolantnr  in  malQim  friabilem. 
Admiattum  laSt%  atiium  vertkur  in  durum  cafeonu 
llltio  :  Cur  nonnuUa  corpora  interjeSa  aliornm  ^oo* 
randam  fibi  coha^reant ,  alia  non  item.  E.  C.  Citteref^ 
qui  expuKa  partibos  oleoiis  no^ium  fere  inter  Ce  nexnm 
nabebant,  adjeSis  fiibinde  novis  oleis  in  maflam  abconi: 
valde  eohcrentem.  Coatra  vero  o^,  atias  Coliii^  ad« 
fastrere  prompta,  interpofita  pii^uedine  non  adhseret« 
Mt*  N.  A.  Omninni  iftorum  ratio  cft  iu  iimitiitts  coha^ 
fimis ,  eorttmqoe  validitate ,  nm  mttm  in  majwi  viciiii» 
tate  molecuiarum^  aue  ptfnSorumm  Nam  iive  e  corpori» 
btts  liqiiefii{(is,attt  candentibus  avolent  corpuCcula  ignca^ 
five  ignif  a&tone  e  molli  iuto  depeliantnr  particulc 

^  «qnes  ,  five  ^ignis  in  corpora  quffpiam  (e  (e  infimianfl 

partes  terreftres  extennet ,  &  (alia  (blvat ;  fiv«  corpot 
qnodconqtte  aliud  admifireatur,  vel  interjiciatttr  aliis, 
iKfflper  particuls  minims  diverfbrum  corporum  dcfe- 
rnntur  vei  ad  iimites  cohcfionis,  vei  ad  diftant!as  repul* 
fionis,  (emperqtte  habetur  diver(a  pun^orum  pofittOy 
&  conjandio ,  qua  fit,  ut  quspiam  corpora  firmiua  co^ 
hxreant  avolantibus  particulis  ign^iSy  vel  aqueis  (quod  fi( 
..  in  metallis  Iiqaefa£lis ,  gleba  are(cente ) ,  vel  interiedit 
^nibasdaro  aliis,  Guod  fit  in'cineribus  in  inaflam  duram 
«oewtibos.    $04  &  fon  noteft»  ut  qu«f iam  interjedhl 


YTff  SiSlol.  CaputlK 

•liorum  (ibi  non  adhcreant,  quod  eren*e,  ii  aqilitn  imer 
dc  (biidum  corpin  interjlciantur  pinguia« 

VII.  Si  cohsfio  pendet  a  locatione  pundorum,  wA 
•ftiolecularum,  in  (k   difiis  iimitibus  cohcfionis ^   non 
4>pus  erit  corporum  fibras  prius  extendi ,  quam  cohvGm 
partium  ruptione,  aut  diflFradione  (bivatur  ;  «tqui  tamcft 
wtendunturprius;    ergo.        Pr.  m-  Ut  primumfott. 
^,  vei  molecuiit  a  limitibus  cohefioms  dimovebumur,*- 
nonampliuscohitrebunt;   trgo.        ^g.  N.  Mt  Ad  Pr. 
D.A.  Puii^a  ultra  otH$m  o>£efwm  Unmfs  dinmd  noa 
«mplius  coh^rebunt  C.  A.     Ultra  ^pr/iwsf  duntaant  N* 
A.  &  Cm.     Plures  in  minimis  diftantiis  daii  cahfiioiHg 
iimites  dixi  §.  ^5^.  Schol.  11.     Punaa  a  limi»  cob«fio. 
Hisdimota  ceffantc  vi  dimovcntc  rcgredi  ad  fitum  prio» 
tem  habct  §.  36.  Thcor.  II.     Siquc  a  limitc  cob»fionii 
dimovcantur  ultra  proximum  limttcm  nen  coh«fionts  ^ 
«eeedcre  longius  ufque  ad  proximum  cohfltfionis  limi» 
tem  ,   docct  cit,  §.  Thcor.  III-     Huc  delata  pun£(a  ire» 
rum  in  theoria  noftni  coh^rebnnt ;  quare  fi  omnis  pai> 
tium  cohsfio  cft  tollenda  i  neceflc  eft,  punda  dimovean» 
tnr  ftltra  onmes  cobitfibnis  limites,  proindcque  prius  fi* 
bras  corporum'  tcndi  oportct,  quam  corpora  ipfc  rumpi^ 
Httit  difFringi.     Tenduntur  vero  fibr«  corporum  nwgis^ 
minusvc,  prout  punffa  vcl  moleculx  ad  majur,  mi* 
iwisvt  fpatlum  fimt  diftrahenda  ,  pro  ratione  fcificct 
Hmttum  cotacfionis.     S«pe  i^iajore  vi  opus  eft  ad  difc 
frinaehda  corpora ,  nonnunquam  minore,  prout  nempt, 
pun^la  ex  magis,  miitusve  robuftls  iimitibus  funt  remo* 
venda. 

VIII.  Cohifio  cxplicanda  eft  pcr  particulas  hama* 
tas ,  &  uncinatas  ,  aut  alitcr  configuratas  ;  non  crgo  pct 

fofitionem  pundorum,  vel  molecularum  in  limitibus  co* 
«fioiiis.  Pr.  A.  Per  hamos,  &  uncos  fibi  mutuo  imple- 
xos  refiftitur  feparationi ;  crgo.  ^*  N.  A.  adPr.p,  A» 
Per  hamos ,  &  uncos  aliquando  rcfiftitur ,  &  rcfiftitur 
fcparationi  pmiutn  mjorum  C|  A.  fcmptr  itfiftitor  ^ 


/ 


\ 


m> 


llirationi  fartinm  mitmnarum  N,  A«  &  Cm.      Ncqu^ 

omnes  parces  majom  coha^rent  per  hamo$,  &  uncos  ; 
mults  eniin  iibi  connedluntur  per  conta£tum  fecundaiil 
fqperficies  p{jinas»  Scd  neque  omnes  minores;  q.uit 
en^in  dicat  omnes  partes  minimas  hamoiene  ,  «ut  un? 
cos  ?  Sint  inuno  hami,  vel  unci  (quod  interea  dabo  )  « 
pcr  quid  cobxrehunt  pun£la  eleipentaria ,  inextenia  ^ 
^T  proptoreaque  omnis  %ur«  expertia,  ? 

IX.  At  per  configurattonem  aliam,  tut  pcrlmple* 
:icioneai  partioia  baberi  pciteft  c.OLhaeiio  ;    ergo.     Pr.  A. 

.  Fiiamenta  variis  du£libus  conttxta.  conficiunt  piuinuni 
fitis.  cohsrentea» ;  ergo>  S^  partes  fibi  implexx  C04* 
j^fc^t  in  corpus  utcunque  firmum.  Canfirma^.  Mi^ 
croCcopiis  Qxpioratum  eft  fibras  carnium ,  ofliuiin^  aliop 
fumquc  corporun}  (Ibi  mutuo  iinglexiis  cflc  ;  erg,o^ 
^f  N*  A.  Ad  ^rob.  C.  A..  D«  C.  ergo  &  partes  ms^Qf^^ 
res  fibi  impicxs  cohbrebiint  C.  Cn^.  partcs  mUnm^^  mtt 
putt^a  eleMeut^ia,  N.  Cm.  Partes  majorcs  figuraffi  \u^ 
bent ;  ergo  per  certam  configurationein ,  vel  implcxiOf 
oetn  (ibl  cohdBrere  pofltii^.  Pun£la  elcmcutaria  figunMH 
Mn  habcnt;  crgo.  adot  Partes  majorcs  fibunet  coOf 
Sic£ti  per  figurain  docet  cxpcriciitia  ;  quat  pri»  mioiioi^ 
nioleculis ,  aut  pnn£lis  clcmcntaribus  nuUa  bab^ucb 
M  Coufirm,  D.  A^  Non  tanien  CKploratunil  cBty  impl^ 
xioncm  iilani  caulam  cfic  cobsfionis  C.  At  fimilqfMI 

.  tdud  cxploratum  fuifyN.  A.  ^C. 

\  %'  Fig^ra  ni^io  c0c  potsA^  ^uv  partcs  corporis  fk* 
cilius  ab-inviccmdivcllaiiitur  (hiac  nempc  nd  fepaisatic^ 
ncm  partium  utimur  inftrumcntis  acutis.,  c.  c«  ^hro^ 
acH  &c. ,  non  vcro  obtufis ) ;  crgo  etiam  figura  mitt 
cft,  cuc  p^tcs  cohATC^C ;  ndo^contrariorum  cadcm  cft 
ratio.,  ac  diCqipliiM*  Jjt.  C>«  A.  Figura  cft  raritK  cfoafih 
lialis  C.  A.  fhmalk  Np  A.  . Sic D-Cs.  &  N. Cm.  Cut 
jf^toi  fipartttmr  >  ratio  fibr^salift  cft  in  vi  rep ulfiva,  qus 

4Al«cts  ii^  iniotifiis  4ift4ntw  iniixuwiitii  ^ubct  pai^ttt 

H  5  ^  r  f^if^A- 


t 


flS  ScSiot  CAfutW. 

diflToriarf.  Car  ficiliia  Jiparmmr  ftdbtbttts  tnftrmien- 
tis  acutis  ^  tn  cau(a  eft  >  quod  tn(h*ttmentorain  acief 
refpondeant  parres  \>innino  pau»/  ac  prainde  modica 
liabeator  reiiilenria.  Seqoitar  .*  minus  virium  impendt 
in  faperMldam  re(i(lemiam,  plns.  contra  in  fepararionetit 
partiirm.  Hinc  illa  factHras  (epararionis.  Qiiod  de 
€Of»rari»  additur,^  (ic  inteHlgendum  :  contrarta  pcrtxne* 
ve^d  eandemdifcipHnam;  nrni  tanquam  fi  in  contrarits^ 
cidem  iie  ratto  quaHtatttm»  proprietatum^  ac  viriam. 

^  XL  Ex  &la  coltoearione  latenmi  ratidtts  Grpe  for. 
Hix  eonfurgit;  ergo(imtKter&  corpttsex  Iblo  partium 
fitu,  eoqae  independente  a  rtribus*  l}t«  Tt  A,  N.  Cm. 
Sspius  dixii  diiUnguendttin  eife  partcs  inter  ffu^t^rts^  6e 
miiHmttf.  Sed  neqtie  partes  fornicis  majorcfr  foU  coilo- 
catioiie  vaHde  fibi  cohcrent;  oportet  )acere$  inter,  6e 
laptde»  mittatur  eahc  aqQts ,  dc  arena ,  ve)  Tofo  fobada»^ 
Eft  mitem  m  tofe  y  ff  artw»  muhttm  vhrioU  ,  ht  talct 
wultutn  falis  afcalhti  ^  qtti  bim  fahs  m  aqua  Jhlvuntur^ 
in  fi  agmtt  (  cntn  aher  fit  aeidus ,  aitter  aicahttut } ,  p^« 
tetqtie  terrefiret  valde  attetmmn\  frtecipue ;  Jt  Imgo  tem* 
fore  Jiki  relmquwimr;  itt  maffit  tum  aqua  fitba^ay  Cf 
jrequenter  pemti/id  fecum ,  0e  aghof^  evadnut  tandem 
fenm0mai  idcirco  inter  ajperat  laterum^  hfidumve  fth 
ferficht  poja^  accurate  fatis  $0va  impknt  ,  poiroi  higre^ 
diuntur  y  contaBtHn  Jitpei^eierum  ^fic  adaugent  y  ut  coha» 
rcntia  inde  firnH^ima  oridiun    Hii  Mufchenhroekhs^ 

XII*  Hat^ra  qttiete  pftrtinm  habetnr  eohitfio ;  er# 
go  a  qutete  parttam  repetenda  e(i  eehcfio.  FroK  A. 
Pofico  tnotu  inte(ttno  partiam  non  babetttr  coteHo ; 
«rgo  eic  oppo(iro  habit*  qniete  parttam  habetar  eohar- 
fio«  Confirmaeitr  h  Pluida  minttsr  cobd(renr,^iam  (oH- 
da,  iqiiia  fiutdorum  partips  niajori  niotai  bbnoxiat  fitnt ;. 
f  rgo.  Confirm,  II.  Ideo  partes  aqdW  glactars  colisrent 
magis,  qtiam  non  glaeiatdt,  ^aia  (rigore  con^faringttntury 
fi^up^^ofiri^.miaasiiiotentari  «rg^      }|(.  O.A. 

^'  babi* 


/ 


"^    Lix  virium.  IT9 

iMbita  qnitte  parttinn ,  iif nulqae  viriius  dijlraffioni ,  ae 
€ompre£iom  refiflcHtihiS  hftbcrdr  cobcfio  C.  A.  habit« 
{•lam  quiete  N.  A.  &  Cm*  Ad  Prob.  D.  A.  Pofiro  mo- 
ta  inreftino  partiam  non  habetor  cobxfio  arguitivem 
T.  A.  fwnudinr  N,  A.  &  Cm.  £x  moto  qaidem  in* 
teftino  parttum  arguitor  nuUam ,  vel  certe  modicam 
'  baberi  cohrfionem  in  corporibuSi  quia  partes  motn  iilo 
•girarc  non  habenr  vim  coh«fivam  fiitis  expedftam ;  fe» 
rantnr  enim  vires  ab  impoifione  particularam  ignea* 
rum  motam  hunc  ctenrium  y  qua  impulfione  ceflante 
rttrfuro  particalascohsrere  necelTeeft,  non  obceffantcm 
fmotum ,  (ed  ob  vires  fnagis  exfeditat.  Dixi  T.  Ntm 
cum  omniam^corporum  moleculae  motu  inteftino, 
feaiperque  agiremur,  &pe  tamen  firmiter  fibi  coharrent. 
Ad  Confirm.  I.  N.  cau(alem  i  minoris  enim  cohsefionis 
canfii  eft  ipfa  Auidorun^  figura ,  ievitas  &c.  de  quibus 
proxiine.  j4d  Coufirtn.  IL  Iteram  N.  caufiilcni :  icili* 
cer  rario  formalis  eft  in  viribus  magis  expediris. 

XIII.  E  phsnomenis  evincimr  muruum  partiuhi 
contadum  /ecundpm  planulas  fiiperficies  canGtm  cfle  co* 
hcfionis ;  ergo.  Pr.  A*  L  Corpora  Isvigata  (ecnndum 
plures  fuperfiQiei  partes  Cc  contingunt ,  indeque  faciiiot 
(ibi  coha^rent,  qnam  non  larvigata.  II.  Eadem  ex  ra- 
tione  globuli  duo  plumbei  fibi  non  adhai^ent  ;  adhx* 
rent  autem  plana  duo  eylindrica,  vel  marmora  lcviga* 
ta,..aut  iamins  polits*  III,  Ut  primnm  gutta  guttant 
CQniJngit,  c,o£unt  amb«  iii  unam«  1V#  Nivis  partes  quo 
niagis  per  eomprefljonem  aut  CeCemxiw»^  ^^  CoUdtt 
quarcunque  contingunt ,  hoe  magis  adbf^rem  ;  ergo* 
^.  D.  A.  Evincitur  contadam  efie  cau(im  occafionalem 
fcobefionis  C.A.  formalem  N.  A.  &  Cm.  Eft  &pi 
contadus  phyficus  t?3era  occafio  exerendae  vis  cohsfivsr  ; 
nam  fieri  poteft  (6t  immo  plerumque),  tit  contaaa 
illo  phyfico  deferantur  partas  ad  eiusmodt  diftsmias  mi- 
nimas,  in  quibus  habencui^  limites  coh^fionis.  Fit  ^ 
io^aoiy  iftud  pkruQiquc;  im»  enini  fitri  fimftr  {docct 

H4    ^  ^.   tSltt* 


I20  SeSUh  tapAlf. 

•4)iia  oieofic ,  sat  pmgQibus  afpcr&  ,  fnitfiit  mii  aA» 
hacret,  Ucet  (enfibiliter  eas.  contingat.     Hinc  facins  e« 
ruitar  refponfio   ad  ph^nomena   fingolariter  addudA» 
1.  Lcevigats  iaminz  fiiciiius  cohsrrem ,  ac  fortius,  quia  > 
iecnndum   plures  jkperficiei  fartas  (e  (e  conungunt^ 
proptereaquc  plures  virtutem  cohatfivam  exerunt.     Il-« 
Non  sque  fibt  adhsrent  globi  dno  plumbei,  ifuia  iii, 
paueis  admodum  pnndiS'  vt  contingunty  non  tgitur  m«  - 
fi  modica  vis  cohji&iionis  exeri  poteft.     lli«  (iutt£  (e^ 
contingentes  coaunt  in  unam  ,  ac  tnm  fibi  col^arent , 
quia  reiiicet  ad  limitcm  cohitfionis  dclars  fuehnt  C.  A« 
quia  duntaxat  (e  contigerint  N,  A.  ^  Cm«     iV*    Nirit 
partes  hoc  magis  Hbi,  aut  corporibus  aiiis  adhsrent  ^ 
quo  magis  comprimuntur;   comprefiione  enim  defc* 
runrur  ad  yaiidioret  cohxfionit  iimitct* 

XIV.  Hemifphma  Mtgdcbar|(ic«  tSrc  intemo  ▼!• 

duata  per  JQlam  aifris  externi  prejjiouem  tam  vaiide  co» 
lisrent ,  ut  in^ciitibus  adhibitis  virihus  xgre  ab  invi- 
cem  divelli  poilint;  ergo  colidio  rcpeti  poteft  a  prc- 
mente  aere  extcrno.  ^,  T.  Af  CuiA  cnim  difia  he- 
jmifphXiia  fprcius  cohxreantf  quam  premcre  poffit  a^ 
incunibens ,  per  filam  a^irM  prejjionem  non  cohsrent. 
D»  C«  ergo  cohsfio  partium  majorum  repeti  poteft  ft 
premente  aereC.Cm.  Minimarum  N«Ci^.  Si  ex  ca* 
vitatibus  hemirph^riorum  exhauritur  ter  ,  cohcrent 
txtra  vactmm  Boyleamm ,  n^i  tamen  in  vaeuo  ,  nani 
recipienti  impodta ,  &  exfit&o  aifre  pmiii  cominuodif^ 
folvuntur;  ac  proinde,  qoia  liabito  tcrc  coherent ,  de- 
ficiente  vero  non  cohserent,  acr  premcnt^ohsefionis  cau* 
la  eft.  At  minimx  corporum  molcculs  tam  in  vacuo^ 
qbam  extra  vacuum  cohatrenti  nequc  pb  aeris  dcfc£Hin| 
diffociamur ;  crgo.  i 

XV.  In  vaeuo  Boyleana  «ther  fiibeilifllmut  omnit 
corpora  prement ,  minimas  'corporum  moleculas  com«* 
ficimcr^  f  oici^  i  trgjo  Ctltcm  tb  mticrc  pcpdct  colMtfip* 

/ 


N. 


Ifl^.  N^  A.  Cam  «nim  dether  rubdliffiim»  ponatur ,  exlt 
lcs  utcunquc  poros  corporum  pervadet ,  partesque  mi* 
liimas  dijlhivet  potius,  quam  eontprimet,  .Denique  ({ 
jem  ioterea  partes  (biidorum  cohsrere  per  aeris ,  vel 
jrtheris  pceffionem ;  at  per  quid  cohcrebit  aer  ipft,  vel 
irther  ?  an  per  aiium  denuo  aerem  ?  itque  rurCim  pet 
^liumi  ^  (ic  in  infinitum  ? 

vXVI.  Si  partes  miniois  cobsrerenr  per  aertm 
comprimeqtw,  non  (equeretur  proceCTus  in  infinitnm  ; 
crgo  cobsfioxiia  caufa  eflle  poteft  aer  premens.  Pr.  A, 
Partes  aere^  cohsrere  pofTent  per  reroetipias,  (icurpar« 
tes  glutinis  perfuammet  viteoiitaiem  (tbi  cohcrent. 
IL  Fartes  fluidi  aerei  funt  re  ip&  dlfTociati^  nen  crgo 
Opus  eft  v'\  uUa  Gomprimente,  ])t«  N.  A.  Ad  Prob« 
D.  A#  Cohcrere  poflent  per  (emet  ip(as,  b.  e.  per  vim^ 
q\ix  partibus  ineft  C  A«  fine  vi  N.  A«  &Cm.  Etiani 
gtutinis  partetficper(emecip(ascohxrem)  ur,ntfi  in  li« 
oitibus  cohsfioniii  locjitflr,  cohxfiirse  non  fint»  Ad  IF* 
D.  A;  Majares  fluidi  terei  paries»  &  folum  aliqnx  fiint 
re  vera  diifociats  C,  A*  Minima^  aut  mtjores  omaea  N^ 
A.  &  Cm, 

XVIL  Sine  attradione  non  habttur  coh«(fo  ;  tr^ 
go  tttrAdio  caufii  eft  cohsfionis.  ,  i;e-  tmo.  Ctiam  & 
ne  repulfione  non  obtinet  cohncfio  (  vi  enim  et^hsefionit 
sum  iUfiraBioni  modo  rtfiftitur,  (ed  &  eompreffimii  par» 
tium  )  ;  cur  noO  in  reputfione  nm  cofaftfivtm  (tatuunt 
Keutonitni  ?  l|t.  ido«  D»  A«  fine  atrrtdione  itoffara 
finfi»  inreUeda.non  habetur  cohsfio  C.  A.  Neutoniano* 
rum  (enfii  aecepta  N.  A*  &  Cm.  £  Neutonianorum 
doilrine  debereor  partes  eorporis  denfioris  flrmius  co« 
barere,  quam  minusdenfi  {\,  prs(enr.  Coroll.  11«)  | 
qisod  fiillit ,  ut  videre  eft  in  tnrO)  di  adtmtfitt. 


H5 


1 


ISS  Se3i0  T.  dput  IV. 

§.  49*  Mobilitai  eft  ga  affeSio ,  fua  eorpus 
iftum  redditur  vi  propria  loeum  mutare.  In  ex- 
plicandis  ejus  ph^enomcnis  necelTum  non  eft. 
«d  curiram  noftram  confugere.  Sed  tamea 
pauci^  de  illa  agam. 

SehoL  t  Netno  non  ridet  diftingQendain  efle  mo*] 
imi  inter  eommmitn ,  &  proprium,  Morns  eommunie 
eft  nnitirio  loci  profeda  a  principio  mere  evtrinfeeo, 
non  modo  td  motum  determinante ,  (ed  &  mutatio«~ 
mm  loci  elficiente.  E.  c^  cum  quts  in  navi  €on(idens,ae 
qniefirens  provehitnr  eodem  motii,  eadem  celentare ,  dc 
diredione  eadem  ,  qua  navis ;  aar  duro  eorpas  mana 
transfertnr  de  loco  alio  in  alium.  Motus  propriui  dt- 
citbr  mntatio  loci,  cujus  ratio  ftiffictens  eft  tam  in  prin* 
cipio  aliquo  extrinfteo  ad  motnm  determinante »  qoam 
ih  ipfi)  corporemoto  mutationem  illam  efficiente  ;  e.  c« 
dum  iapis  manu  ejettus  progreditur ,  progreHurns  in  in. 
initum»  nifi  &c.  Non  hic  de  mota  comoiam  difcepta* 
|>o  f  icd  de  proprto. 

Scbol^  IL  Moeus  ifflpoflibiiititem  adftroere  rifi 
iunt  yer^r/bs  qoidam  Philo(ephi,  qoorum  arginias  (  Keil* 
lius  vocat  ineptiat )  breviter  referam.  i*  Diodoruo 
Croum  apod  Soxtum  Empiricum  fic  arguir  i  Quidquid 
movctur ,  aot  roovetur  in  eo  loeo,  uhi  eft,  aut  ubi  non 
e(L  Non  poteft  moveri  in  eo  loco,  ubi  eft;  nam  ibi 
manet,  &  quicicit ;  motus  autem  eft  mutatio  loci.  Sed 
neque  poteft  moveri  in  eo  loco,ubi  nen  ^;  nibil  enim 
inutari  poteft,  ubi  nondnm  cft  i  ereo,  iqe.  Nec  eor« 
pus  movemr  in  loco,  quo  cft|  nec  m  loco,  quo  non  eft, 
ied  ipovetor  de  loco  in  locum.  Cauziut  inquit :  motus. 
eft  mutatio  eoexifietttia  eorporum^  In  mutfttione  bae  co« 
exiftentia  ona  amittinn*,  altera  aftumitor.  Eodem  igi- 
tor  conata  corpus  motam  relinquit  locom  onum ,  6c 

«Iteram  attiogit.    II.  &fi0iiar  «rgmiWQniini  qood  ^cAf £> 


I 


/ 


lix  vMurm    '  MJf 

kf  nomine  infignivit,  ab  Ariftot.  L.  K.  Ttyfi^.  e.  9.  hone 
in  (enfuni  reciratur :  £x  eo  toilitur  motus,  qaia  nun- 
quam  id,  quod  celerrime  currit,  confequetur  id,  quud 
f ardius  currit ;  id  enitn,  quod  infequitur ,  eo  primum 
perveniat^  ne^efleeft,  unde  id,  quod  fugit,  fngam  arri* 
puit.  E.  C  ponamus  teilndinem  ao  paflibus  prsiviite 
Achillem.  Sit  vero  Achillii  celeritas  vicles  major^quam 
eAudinis ;  (ea  ut  00  s  i  •  Qub  tenrpore  AchtUes  de« 
curret  pafTus  tto  1  teftudo  decurret  unum.  Nondjam 
igitnr  Aehiiles  telhidinem  aflecutus  eft»  Damque  A« 
chiiles  emccietur  viceiimum  &  pnmum  paflTom » teftu^ 
€lo  interea  conficiet  vicedmi  fecundi  paflfus  partem  vice- 
(imam.  Atque  cuiti  hanc  vicefimam  partem  paflTus  vx- 
cefimi  (ecundi  attigerit  Achilies»  percurret  teftndo  vw 
cefimam  vicefimie  prtoris  \  fic  v^ro  progredi  Kcebit  tn 
infinitam,  Quare  nunquam  AchiUea  teftudinem  eonte* 
qa\  poterit.  At  enim  objedio  Ji9C  fopponere  videtur 
divifibiiitatem  materi^intinfinitum,  Failit  luppofituol 
(  §•  46.  Schol.  II. ) ;  igitor  6c  bbjeaiof  Re(ponfionem 
laliam  qui  volet»  KitUinm  cmC\3}%u  \\l%  Aiii  fic  ar- 
guunt:  quidquid  movetnr,  aut  movetur  in  termino  a 
qnoj  aut  in  termim  ai  quem ,  .aat  qnando  eft  in  tttroque 
terminoi  Non  autem  poteft  moveri  m  termhi»  a  fn^, 
fiam  quamdiu  in  illo  eft,  qote&tr.  Non  t»  termino  ai 
qttem ,  cum  ibi  motus  fit  abtblntus*  Non  in  utrei/pH 
tcrminoy  alitcr  enim  corpt^  fimul  occuparet  duo  loca  ^ 
cflctque  roajua  (e  ip{b.  ]^.  Matus  ex  eflentia  fiia 
cft  fiiccejpva  hci  mutatio ;  aon  ergo  peragttor  unico  in* 
ftanci,  neque  iu  unico  termino ;  ied  in  termino  a  qno 
incboatur  motuSi  in  mcdiocMi/fxffiMwr,  in  termino  acl 
quem  fOrfiekur^  .  |V.  Nonnnlti  fic  oppofiunt :  Si  im« 
poflibiiis  eft  major,  aut  minor  motos  celeritaa,  tum  imi* 
poflibilia  erit  &  ip6  motus ;  atqui ;  ergo.  Pr.  xnu 
Aut  UHO  momento  maior  celeritaa  plora  tpatii.  punfta 
pcrvoiat,  quam  cderitas  noinor,  aotpercnrrtt  totiden« 
Sx  plora  :  tam  anom  momentnm  eft  d^ifibile  in  duni. 
li^nes  ^oribos  %itii  pw&ii  rd^oadciKes  ^  ^uod  |1k 

-»      fc^dum 


fS4  SeSUl  CtputtF. 

Ibdura  eft;  mMn^ntam  <|uippe  dmtatmi^m^iiftmih. 
Si  rotLdem  ;  tum  oclcritas  crit  xquaiis  tjrditati  ,  qiioj 
ibfurdiiliraQm  efl.  Re(pondet  Caittiuf  ;  ^mt  oirgtMmi^ 
p^AjftppoMit  Jpatium  abjolutum  a  rebusfeparatum,  ^io4 
fuiAAuoifif  repudiatnr,  uos  nouferh.  Ait  t^o.  \n  eoc 
pore  celerias  moto  haberi  majores  eonatus'  piimitivoiL 
_|ii»utandi  iocum^  qui  ipfi  conatus  rofpici  poflTunr  ntjjtam 
^efpoQivi  funBfi,  in  quibaa  tamen  bab«tuf  diverlifei,  iHMt 
fKttofioais,  fed  gradium  iu  vdrikut^  y 

§.  ^O.  Carjfora  omms  funt  moUUtate  pr^/ 
ditd ;  feu  :  datur  in  corporibus  vij  motrix.  Pr, 
Mo{us  quorumvis  qorpornoi  c^  c  proj^^oruiB 
habec  racionom  fui  fuilicienc^m  in  ipn&  cMr 
poribus  macis;  acqtii  harcrAtionon  eft  alia» 
^uam  vis  mocrir  ;  ^ergo.  Pp.  M.  Motus  ille 
repeti  non  poceft  a  manu  projtcicnte,  qu«  li- 
cec  corpus  cjeiaum  non  infequacur ,  tiabecuf 
tamen  motus,  II.  adfcribi  nequic  a^ri  antcrior 
ri,  qui  mocum  potius  impedic,  quam  cfficiar« 
Non  etiam  aShri  po/imori  premeoti ;  aer  eainai 
sneerior  tsncum  refiftit ,  quaiacum  pofterior 
premic;  ergo^  Addam  r  fi  aSrt  rribuitur  vis 
alia  corpora  raovendi :  cur  non  &  corporibus 
aliis  vis  Ccft  movendi,^  Ipcumque  vircuce  fii^ 
iDUcancii? 

ScM*  Offaiii  (bleat  (ei|qenii4  :  I.  Corpora  GiWk 
ififirtia^  tten  ergo  geodisDt  vi  propria  lootrH^eb  j^ 
B.  A.  Sont  inertia  ,  Jb.  e.  ncm  habent  vioa  (e  dbtermV 
Kindi  ad  motuni  C.  A.  tanquam  fi  Qmni  prorlii»  vi  (ine 
daiiisuta  N.  A*  dt  Cot»  N.olkim  avqpvkt  movetar,  n$ 
]iiMua  ab  erite  omftmw  $d  mociini  daserminctiir*    M 


*** 


tex  vlrium$  1^5 

Ya  Inovetitnr  al)  extHnfcco  i  crgo  ipfa  ft  (e  non  tQovcnt« 
^g.  D.A.  movcmur,  h.  c  aliundc  ad  motum  dctcrmii 
toantur  ۥ  A.  Non  gaudcnc  vi  propria  motrice  Nt  A. 
tSlCm* 

IL  Si  corpocibus  infit  vis  motrix,  non  fttii  diftim 
gnitur  fpiritum  intcr  &  corpus;  fpiritmm  cnira  pro*. 
•rium  cft  moverc  fc  ipfes,  corpomm  vcrb  roovcri*  ^ 
_7.  A.  Caufalem  D.  Spirituum  proprium  cft  movcrc  & 
ip(bs  cx  dctcrinmationc  propria  C.  A.  aliena  N.  A.  SC 
Cm«  / 

III.  Si  corpora  omnia  moventur  ab  intrin(cco , 
Vivunt  omnia ;  non  autem  vivunt ;  crgo,  Pr.  M.  Vive. 
rc  eft  movcri  ab  intrinfcco.  IJt.  N.  Scqctfl  M.  Ad. 
Prob.  D.  A.  vivcre  cft  movcri  ab  intrinftco  rootionc  vi- 
tali,  qualis  habecur,  cum  anima  mptarur  per  cogniiiO; 
ttSf  &  appccitioncs  C.  A.  mocione  locaii  N.  A.  &  Cm^ 

IV.  Illud  dicj  dcbct  caufi  irictus^  per  qnod  corput 
detcrminatur  ad  ccrtam  direaioncm  ,  &  cclcritatenl 
(qus  duo  prscipnc  io  motu  funt  refpicicnda)  i  atqui 
pcr  impcium,  aut  impulfioncm  extrinfecam  corpus  dc* 
terminatur  ad  ccrtam  direaionem ,  &  ccleritatcm  ;  er* 
go.  K*  D.  M.  lUud  cft  cauGi  motum  detcrminanl 
Cf  M.  cfficicnsN.  M.  C.  m.  &  N,  Cm.  Cauia  motum 
efficiens  ideft,quodmutationcm  ibci  cfiiclcnter  inducit« 

V.  Corpuf  mottim  in  motn  perfevcrat  per  vim  in« 
ertis ;  non  ergo  movctur  pcr  diftin£lam  vim  niotri« 
tcm.  ^.  D.  A«  Corpus  motum  inovcri  pcrgit  pct 
vim  inettice,  tanquam  pcr  caufam  quafi  determinantetH 
torpus  ad  priorem  diredlioncm ,  &  ecleritatcm  C.  A. 
rflnquam  per  vim  cfHcientem  motum  N.  A.  fic  Cm« 
Corpus  in  motn  poiifum  vi  inmic  dcterminatur  ad 
confcrvattoncm  prioriscclcritatis ,  &  diredionia;  vi 
•tttcm  motricc  x c  vcra  movctor. 


/ 


VI.  In  corporibus  delabcdtibus  acccleratt  motttS 
caafi  eft  vis  attratliva  ;  non  ergo  vis  motrix.  ^.  £tU 
am  Vis  hcc  attra£!iva  (blum  dcterminat  vim  motricem 
ad  majorem  ,.  vel  minorem  ceieritatem  ,  pro  ratiooe 
diftantiarumt 

VIL  Aeri  prementi  tribuitur  •{cenfiis  Mercnrii  in 
Barometro  ;  ergo  (imiliter  aeri  a  tergo  impellenti  tri 
buendus  eft  motus  corporum.  ^,  C.  A.  N.  Cm^' 
Di(p.  eft  :  Mcrcurius  infra  exhauftum  non  a(c«ndit,  nce 
snanet  sque  (iilpenfus ,  ac  ex^ra  vacuom  ^  (ed  in  vacuo 
ad  libellam  (e  componit ;  ergo  a(cen(]o  ,  aut  (urpen(io 
Mercorii  rcpctdnda  eft  ab  aere  premente.  At  corpora 
perinde  in  vacuo  moventur,  ac  extra  illud  ;  crgo  motus 
l^orundem  ab  aere  profici(ci  non  poteft.  ado.  In  Baro* 
metri  parte  (uperiori  habetur  vacuum  Torritellianum  , 
^uare  aeri  inferne  prementi  non  reiiftitor  ;  poteft  ita- 
quc  prc(fio  aeris  in  Baronietro  fuurn  (brtiri  efreftum* 
Ar  cum  e.  c.  Upidem  premit  aer  pofterior ,  tantundetn 
rc(iftit  aer  anterior  ;  proindeque  iapis  ip(a  aeris  prciEo» 
Vtc^  ac  reprclEonc  confiftere  deberct,  non  movcri. 


.  «       * 


Vjin.  £olipiIa  rotulis  mobilibos  impofita ,  &  ex- 
cuITo  bperculo  regfediens,  aut  pyroboius  acceniiis  iii 
altum  Inblatus ,  vel  tormentum  exoneratum  verfus  fun» 
dnm  redtens,  non  moventur  vi  propria  ;  fimiliter  neqne 
corpora  alia  movebuntur  motu  proprio.  ^.  C.  A* 
Kf  C.  vapvr  tnim  viokfite  tofnfrejfus  pretnit  in  furtes 
^>miies  in^etu  ^tfuabili  ;  wtnque  fer  4iperturam  Ubert 
^rumpere  poffit ,  toUimr  ex  ea  parte  preffio ,  atque  its 
fravalet  var  iu  partem  contrariam ;  verba  (unt  P.  Mahi. 
Hinc  Ut ,  ut  JEolipila  ,  &  tormemnm  rcgrediantut , 
pyrobelua  In  altum  feratur*  At  fimilis  ratio  non  pu« 
gnat  pro  ^mmim  corporibus ,  quantumvis  fatcar  «m 
fniCM  fnoveri  motu  fivc  communi ,  Gve  mere  ab  extrilip 
wco  proveoiattto. 


\ 


Lex  vMum.  1^7 

^•51.  hertis  tjt  frofrieW;^  ^M  tcrpuM  fi» 
motum  >  fiu  ifuiffiens  fidtum  fiium  eonfirvat ,  if 
csufa  ixtrinfieis  fiatum  illum  mutarc  cmmttibus  rcm 
fifiit.  Hinc  vis  inertia  aliquibus  dicicur  fris$* 
Cfpium  confirvanM  ftatum  ;  aliis  frtHcipium  refU 
fiendi  mutationi  fiatus.  Nos  ifl  data  defcriptio« 
ne  conjunxTfnus  utrumquc» 

Schof.  Sant,  qui  pfo  priocipio  refifietuU  mueasiom 
Jhtus  dicant  frinciyium  refificndi  fnottti*  Verum  id  ge- 
nos  inercia  convenic  dttncsxac  corporibus  quie^centibos^ 
non  autem  in  mota  conftimcis ;  nifi  forte  dicaot  \n 
iftis  inertiam  eflc  principium  refiftendi  fnowi  acaltrat^ 
do,  vcl  rctarioHdOj  zvx  frorfus  exfiinptiudoy  yAmoeui 
aUeuo* 

§.52.  Refifientia  ^  qaa  caufis  extriQfccis 
llatum  corpomm  imroutare  conantibus  rei]fti<« 
tur ,  efeffu  fieo  non  caret  ;  corpus  enim,  (]uod 
ftatum  alterius  immutat,  (emper  aliquid  Ja 
^uaniitate  motut  fui  amittit,  quia  (emper  cele« 
ritatis  partem  amittit ,  ut  amplius  patebit  ex 
dicendis  ad  matjprtam  ia  imfaHu^  incur/u^  6c 
occurfu  corporum»  Haec  cckritatis  diminuiio  tU 
feAus  pojltivui  eft ;  4  vi  itaque  fofitiva  proc^ 
dac  >  oportet ,  quaai  imrtiam  1  vel  refiftcnUam 
ascimus* 

%.$^.  Dupliciter  fpeftari  poteft  vis  in« 
erfic  :  !•  ^uaunsu  dicie  nudum  conatum  conferm 
vanM  fiatumjiium  ,  ejusquo .  mutationi  refifiendK 
IL  prout  a^uaU  oxercitium  vis  iffiut  defiffige. 
Priori  modo  fiimtam  dicunt  {choldc  vim  inor^ 
tue  ina&ulmo^  pofteriorc  vtro  iMt^Ca  acceptaoi 
vimiso  uHuIUo^ 


1 


ff.  54*  hfrth  in  aSu  Imo  frop^rtimdu  ifi 
mtfis ;  non  enim  corpas  fismiJum  sliqugt  tm^ 
fum  fai  psrtei  ftarum  fuum  confervare »  ac  rou* 
fari^ni  refiftere  mcitur,  CedficunJum  omneu  In 
pSu  lUofumf^  proportionatA  cfi  tsm  ms^^  fuum 
impetui  fsBo  ab  agenre  extrinfeco  ad  novum 
fiarum  dererminaote  ;  readto  enim  ieaiper  ^ 
«quaiis  eik  debec  adipni  (  $.4.) «  *^ 

CoroU,  L  In  eodeoi  corpore  mafls  inafiet  eadetn. 
Qmire  vis  inerriis  in  s£hi  loio  (utnjmi  (einper  in  roc-  ^ 
pere  eodeni  manet  irqailis,  &  eadem.  AQiones  cor* 
fOfftmftxtraneorum  diver&  flinr;  liinc  visinerriir  in 
a^lo  Ildo  confiderata  diverfa  eft  in  eodem  cocpore  y 
jamque  magis,  jam  tniniis  exerirur. 

CoroII.  11.  MalTa  eft  quantitas  mareric ,  ex  qu 
nnum  quodque  corpus  coagmentator.  Matetis  COrpo* 
rom  funt  pun£ta  eiementaria  ;  quare  fi  maflis  conftanti 
proportione  relpondear  vis  inertia^,  refbe  inruleris  s  eAtn 
eriri  ab  inertia  fingulornto  punfiorum  mzffim  conft^ 
mcntinm» 

* 

§*  5^5»  Corpors  omms  funt  vi  inortiu  pr^m 
Jtis*  Pr,  Experientia  compertum  e(l  I.  viia 
qaamcunque  mintmam  non  (lifficere  corporl 
cuicunqueimpellendo^ac  mpvendo.  II.  mo» 
vendo  corpori  graviori  majorem  vim  efle  ad- 
faibendam,  minorem  leviori.  IIL  nunquam 
corporibus  morom  conciiiari ,  aut  in  iisdem 
fifti  abfque  viriom  »  &  celeriraris  difpendia 
in  corpore  impingente  »  vel  motum  fiflente» 
IV.  fi  quis  gk>bom  delabentem  manu  infe^ 
^auAtur  ^  feacirt  dolorefp  ob  refiftentiam  globi« 

Atqui 


h 
^ 


Lex  viriufn$  129 

Atqui  iftorum  nihil  evcniret,  G  corpora  rali 
proprietate  inftruflta  non  efl>nt ,  qtia  ftatum 
iuum  confervent,  ac  refiftant  caufis  extra- 
nets  mutationem  ftatus  inducere  conantibus  j 
•  ergo.  Pr.  m»  fi  corpora  vi  refiftendi  inftru- 
Aa  non  funt ,  poterit  vis  quxcunque  fuum 
forciri  efFedum  j  eft  enim  vis  principiiTai 
^(9ionfs ;  poterit  ergo  corpus  quodvis  vi  qiii-. 
vis  dc  ftatu  fuo  deturbari.  ado  :  fi  non  refi- 
ftunt,  fine  ratione  fufficicme  de  corporis  im- 
pingentis  celeritate  quidpiam  detrahetur,  aut 
dolor  in  manu  corpus  cadens  infequehte  fen- 
jictur ;  crgo.  ^ 

S<;boLL  Philo(bpIioriim  aliqui  vim  inertis  a  cnrpor^; 
bui  ,  6c  materia  excludunt,  opinanres  aliis  corporuin 
proprietatibus  tribuendum  afle,  quidquid  inerti^  tri- 
buitur.  Falluntur.  Nam  L  vfs  ifierti<f  diflinguitiir  ah 
txtenfiofie  tnateria.  Prob.  Major  eft  refiftentia  globi 
flumbei ,  quam  ligwt  ejusdem  diametri ;  immo  ifiinoi* 
globus  piumbeus  refiAit  magis  ,  quam  ma;or  ligneus ; 
crgo  per  extenfionem  corpus  non  determinatnr  ad  r^- 
fiftendum  ,  cum  refiQentia  non  refpondeat  extenfioni. 
IL  Difiinguitur  ab  impenetrabilitate ,  per  quam  folutn 
]>ortfO  una  materi^  excludit  aliam  ab  eodcm  loco  ; 
quarc  fi  corpns  praeter  impenetrabiliratcm  vlm  refiftendi 
non  habeat ,  impingens  materiam  percufiam  fecun)  ab- 
ripiet ,  nihilque  de  vclocitate  fua  amittet  ,  quod  expe- 
ricnti^  advcrfitur»  Ad  hjec  potcft  corpus  ^  alrerum 
B  ad  locum  fuum  non  admittere  ,  quin  ei  refiftat ,  fi 
corpori  ^  ad  (c  accedenti  cedat ;  crgo,  111  Diflingui* 
mr  a  gravitate ;  nam  hafc  folum  refidit  motui  fiirfnm 
tendenti ;  vis  autem  inertiae  refiftit  (ecundum  omnem 
dire£lionem,  ctiam  deorfiim  ;  hinc  fi  gr*ve  delabcns  ad 
vclociarcin  laocum  incitarctuv  ^  rcfiftcrct  /   ^uam  rcfi* 


•N 


Ijo  SeStfol  CdputlV. 

fientiam  colligimas  e  dolore ,  quem  hoxtio  (cntif  ^  fi 
corpus  delabens  manu  infequarur.  IV.  »0»  potefl  vu 
reftfiendi  repcfiMb  aire ,  cum  eriflm  in  vactso  Boyieauo  , 
cxhaufto  jam  aere  ,  corpora  reGfterc  ccrtum  habeamus^ 

ScboL  IL  Falluntur  iterum  Cartefiam  docenres  t 
COrpora  ad  motum ,  &  quiccem  cfle  indi/ferentia  mer^ 
faffive.  IndifFerentiamcre  paiTiva  Vcros,  reaUs^  ac  pofi* 
tivos  cfFe£ius  gigncrc  non  poteft.  ^ 

Scbol  III.  Opponi  (blent  (eqaentia :  I.  Contradi» 
Qionem  impltcac  vU  inertia;  ergo  non  datur.  Pr.  A* 
Quod  babet  vim  ,  non  eft  iners  ;  &  quod  eft  incrs ,  non 
habct  vim  ;  crgo#  Vf.  D.  A.  linplica^  var  iuertia , 
fi  pcr  incrriam  {'ntclligas  atejfe  emnem  vim  C.  h.  fi 
dontaxat  abejje  vim  fe  determinandi  N.  A.  &Cm.  Df* 
ces  :  pcr  incrtiam  inreiligi  dchet  abfci^tia  omms  vjs  j 
tiam  &  vi  aViqua  prfedirum  iit  corpus  ,  iners  non  cft. 
Scd  vero  t  Grammaticidis  dicitor  iners ,  quod  vim  hs^ 
bct  nullam.     Pbilofofbis  aliud  (bnat. 

II.  Vis  inerrix  non  eft  vera  vis  ;  crgo.  Prob.  A. 
Vis  hxc  a  minima  vi  fupcrari  prfteft  ;  fed  talis  vis  noa 
cft  vcra  vis;  ergo.  ^.  N.A.  ad  Prob.  D.  At  Vi$ 
h«c  a  minima  vi  (uperari  porcft,  non  tamen  fine  di(pen» 
dio  virium  in  corporc  impellcnte  C.  A.  fine  ifto  N.  A. 

>  £c  Cm.     lUa  virium ,  ac  celecitatis  jaflura  cffe^lus  cft 
incrtis?. 

III.  Vis  quaelibet.  detcrminatam  fui  mcn^uram  ha«» 
berc  debet;  talem  non  habet  vis  inertiae;  ^rgo.  Pf*  •"• 
Vis  inertia  in  eadem  mafla  agit  pro  rationc  celeriratis  , 
quam  habct  corpus  incurrcns  \  fcd  celeritas  potcft  ia* 
tcndi  in  infinitum  ;  crgo  ctiam  aflio  vis  inerti^;  prcK 
indcquc  etiam  vis  ipfi.  Siqnc  intendi  poflet  in  infinli. 
inm,  nullam  haberct  detcrminatam  fui  menfuram  ;crgQ* 
jje.  C  M.  N»m.  Vi»  cnim  incrtiae  refpondet  maflis, 
Ad  Prob.  Df  M.  Vis  iAcrtia  ia  aAa  fecundo  fumpta  agic 


\ 


Lixvirium.  131 

pro  rationt  celetitAtis  C  M.  in  aSu  primo  (pcfiata  N< 
.  JMi,  T.  m.  N.  Cin. 

IV.  EiFedus  inerti^  tribui  foliti  repeti  poflunt  a  ^ 
repnlfiva  corporis,  ad  quod  acceditur ,  &  quod  act 
snatandum  (latum  urgetur  ;  ergo.  Pr.  Av  Etiairi  vii 
repuifiva  refiftit  corpori  accedenti ;    immo  Ob  repulito* 

''i^  Dem  faabetur  imminutio  ^ac  detrimemum  viriuin  in  ac- 
cedente^  «rgo.  ^.  N.  A.  Adfrob.  D.  A.  Etiam  vis 
repulfiva  refiftit  corpori  accedenti,  inque  eo  vircs  immi' 

^  siuit  (^ro  mtione  diftantiarum  ۥ  A.  pro  ratione  malX^ 
refidentis,  &  a^ione  corporis  mutationcm  inducere  co- 

, ,  Hantis  N.  ^,  &  Cm,  Alia  lege  «git  vis  rcpellens  ^  aiia 
vis  inertia?.  Vi5  repellens  imminutis  in  inHntttim  dt* 
fiantiis  crefcit  in  iniii\itnm.  Vis  inertiae  crefccnto  cor- 
poris  impellentis  aclione  augetiir  &  ip(a.  RepuHiunis 
munus  prsrcipuum  eft  impcdire  immediatum  conta- 
fium,  (eniimque,  ac  veUui  gradatim  exdinguere  corpo- 
rum  acctdentium  velocitatem.  Inerti^  oflicium  eft 
confervare  (latum  corporis  ,  &  refiflere  fui  mutationl 
com  diminu^tione  virium  ^  ac  celeritatis  in  corpore  isn* 

\        feOente. 

Vt  Ex  eO)  quod  vires  in  corpore  impingentc  mi* 
Hotntur)  non  re£ie  infertur  dari  in  corpoi  ibus  vim  tner» 
tiaB ;  ergo.  Pn  A.  Vircs,  ac  motus  minuuntur  in  cor* 
pore  impeilente)  quia  impeUens  alteri  communicat  mo* 

I       '  tum,  noii  quia  altcrum  iners  sit ;  ergo  ex  diniimitinne 

virium  noxx  re£le  infertnr  vis  incr^s.         ^.  N.  A>  Ad 

Prob.  D.  A.    Ratio  tamen  fubcfie  debet ,  cur  ipffl  hire 

^   snotus  communicatio  fine  viribiis  ,  ac  motus  difpendio 

j.  ficri  neq«eat  C.  A.  Non  fubeft  N.  A.  &Cm.  Qu«, 
oro,  hic  cau{a  fubeft)  fi  non  vis  inertis  >  qua  mutationi 
fiatus  refiftitu^  ? 


r 


\ 


VI,  yis  Incrtiac  eft  vis  ad  motum  ,  &  quietem  ; 
Adtalis  vii'repu|aat|  «rge  &.visinertifli^    Pr.  m  Rt* 

i  9         ^      '  pug;l\i^ 


13  r  Seaui  CqutW: 

pugflat  yv^  id  oppQfira ;  (ed  motus,  &  qiiies  fimr  oppo. 
fin  V  crgo.  ]$'  C.  M.  D.  m.  rcpugnat  ?is  ad  mo» 
tam»  &  qiuetem.^f/;»/,  ac  fimel  babenda  C.  m.  Jiiccejjivc 
habenda  N.  m.  &  C.  Ad  Prob.  D.  M.  repugnat  vis  ad 
cppofita  eidem  fubjeElo  C#  M.  ad  oppofita  inter  fe  Subd^ 
repugnat  vis  ad  illa  eodem  temfore  in  eodem  fubjedo 
ftonjungenda  C.  M.  fucceffive  habenda  N.  M«  C.  m«  ^ 
N.  C*  In  eadem  anima  habetur  libertas ,  qnz  ntique 
tris  eft  ad  oppofita.  Dicefs  fi  corpora  omnia  fucceffi^ 
VQ  tendere  pofTuntvin  oppofiui,  libera  func  oinnia*  ^* 
ii  (ucceflive  tendere  poflunt  in  oppofita  exdetmmnati— 
ne,frQfnaC,ScqQ.  ^//Viia  N.  Sequ. 

VII.   Vis  inertis  pugnat  cum  vi  motricc  ;  ergo  fi 
darur  in  corporibus  vis  motrix,  non  diktur  vis  tnertis* 
Prob.  A.  Vis  morrix  eft  conatus  locunr,  mutandi ,  vif 
inertiie  (  (alrem  in  corpOribus  quie(centibus )  eft  cona^ 
tus  locum  confervandi ,   eft  principium  refidendi  mo* 
tui ;    crgo.         ^.    D.  At    Vis  inerriar  pugnat  cum  vi 
motrice,  fi  viribus  iftis  fimul  re(]>ondeant  eife£lus  C.  A. 
fi  fucceflive  N.  A.&Cm.     Ad  Prob.  D.  M.  Vis  mo- 
trix  eft  conatus  locum  mutandl ,  &  vis  inertix  conatuf 
cundv*m  con(ervandi,  tendic  tamen  utraque    nd    effe* 
fium  (ucceflive  habendum  C.  M.  conjnndim  habendum 
K,  M*  D.  m.  arqui  conarus  locum  murandi  pugnat  euin 
conaru  locum  pon^ervandi,  fi  tendunr  ad  effedium  coti^ 
jun^im  habendum  C.tfn.  fucceffive  habendum  N«  im.  flc 
Cm.     Nunquam  vis  inerris  ,  (k  vis  morrix  in  corpore 
quie(cenre  fimul  (brriri  poliunt  efFeclum  ;    nunquam 
enim  ambs  fimul  funt  expedirs  ;    quamdiu  vi  inerrids 
pergit  corpus  quiefcere ,  vis  m«trix  ejus  non  e(l  derer- 
minara  ttji  cerram  dire£tionem ,  &  celerirarem  ;  efl  igim. 
tur  vif  motrix  non  expeditom     Ur  primum  corpns  derer« 
minatum  ad  certam  dire£lionem  ,  &  celeritatem  moveri 
incipit,  habetur  vif  imrtia  vidiir ;  vel  ideo  vis  motriX|  Ql^ 
vis  inertis,  ur  funt  in  eodem  corjlorc ,  fibi  non  oppo« 
&untar  ^  iemjpcr  eoim  liabctm:  Aa  vtt  imrtf^  exffdita ,  EST 

vif 


LexVtrtum»  *3? 

vir  ffiofftx  tn^edha;   feii  vis  tnotrix  ixpeiita  ,  If  vt 

itiertid  vi8a^      Hinc  relpondcri  alitcr  p6tcft  .  Vis  mo* 

-trix  e(l  coiiatus  lacum  matandi ;    eft  tamen  impeditt 

VLS,  antequam  determin«rur  ad  certam  diTe£^ionem|  fit 

celeritatcm  C.  h.  parr»  M.  e(l  expedita  N.  h.  p.  M.     D* 

sdam  Vis  inertiae  eft  conatus  iocum  confervandi  ,  viil* 

]  eitur  tamen/dum  vis  motrix  determinata  eft  ad  cei^tatii 

dire5:ionem\  &  celcrirarcm  C.  2.  p.    Non  vincitur  N. 

9.  p.  M.     Atqui  conatus  iocum  mutandi,  &  confervandi 

fibi  opponuntur,  (i  conatus  utcrque  eil  expeditus  C.  m* 

fi  alter  expeditus  ,  altcr  iirptfditus  N.  m.  &Cm.     ReS 

cadem  cfl  in  corporibus,  qus  in  anima  habente  vim  vo« 

lenJi  y  &  nolendi  idem  ohjei^um  ,  cum  tamen  nec^ucaf 

«^uaiiter  idcm  veile,  &  hollc)  ni(i  fucceflive. 

Vill.  Vis  inertiaB  ptignat  dirc£le  com  vi  attraCH* 
Til ;  vis  ergo  attracliva  cum  dctur  in  corporibus ,  nofi 
datur  vis  incrtis.  P.  A«  Sint  duo  corpora  adeo  l)bi  vi^ 
cina  ,  ut  muttio  vis  attradliva  agere  pbilit  feniibilitcr,  ri 
ihcrri^  conabitur  corpus  A  tueri  locum  fiium ,  vi  autem 
flttra£^iva  conabi^ur  ad  corpns  B  accedere  ;  idem  cft  do 
corporcS;  crgo.  "BjL-  N.A.  Ad  Prob.  C.  i.  p.  A, 
D^.  idam  vi  auteni  attraiHva  alterim  corporif  B  conabi* 
tur  ad  corpus  B  accedere  C  1.  p.  vi  propria  attrahcnt^ 
Nt  2.  p.  A  &  Cm.  ^XTorpus  A  vi  (ua  attraf^iva  non  co« 
tiatnr  ad  alterurfi  accederc;  fcd  vcro  conaturi  ut  alte* 
rum  accedat  ad  fc. 

IX.  Corpora  quic(ccntia  locum,  ilattimqae  (tiafit 
cbnfervarc  ^ofTunt  unc  omni  vi  inertia^ ;  iergo  Altein 
neceflaria  non  eft  vi^  inertis.  Pr«  A.  Corpora  ftatum 
fuum  confervant  ^»f  vi  rejiflendi\  tr^o  Jine  vi  iturMm 
J^»  N.  A.  Ad  Probt  N.  A.  Non  cnim  corppra  ftatunt 
fuum  confervaht  unquam  fite  vi  rejiftethdi^  &d  fubindo 
Jme  aSuali  rejt/tetitia^  quamdiu  (cilicct  agcns  cxtranettnt 
non  nititur  immutarc  ftatum  corporis  (  nam  ubi  noii 
Inbctur  eOio^  ncc  faabcri  potcft  rcadio»  iu  e*  refiften» 

I»  lia. 


1^4  '     SeSiof.  CaputJV.     r 

tU,  C^  Incftfl  ftdaalis  )  vis  tametr,  ac  potefttf  refiiUn^ 
haberi  poced  femper,  qaamvis  non  (emper  acta  reii* 
ftatur.  Ad  hicc  :  (i  ^mnis  conrervatio  ftatus  eti&m 
Adio  qutpiam  dici  poteft  ,  cur  dici  non  poidit  i  iner« 
tiam  Tuo  mo^o  agere  luiii  quoqo. ,  dum  fiihil  «dcA, 
^Qod  corpus  ad  matacionem   itacus  (^licitet. 

X.  Corpora  omnia  funt  indiflTerentia  ad  motum  ^ 
vcl  quietem  ;  (cd  indifferencia  non  refiftunt  mutationi 
ftatu&;  er^a  nullA^orpora  reGftunt  mutationi  (latuSy  ac 
pruindc  n^ilia  corpora  gaudent  vi  inertiae.  ^.  D.  M* 
Corpora  omnia  fant  indifferentia  ad  motum,  vel  qaie* 
tem  ancc  decennlnacionem  factam  ab  agente  extrinfeco 
C.  M.  poit  determinationem  Subd.  funt  indifferentia 
Iioc  {enfu,  quod  ncque  motus,  nec  quiesiitd^  natoracor^ 
poris  C.  M.  tanquam  (i  corpus  jam  detcrminatum  noii 
rciiitat  mucationi  (tarus  N,  M,  D,  m  ftd  mrc  paffivg 
iudifferentia  non  reiiltunt  mutationi  itatus  C.  m  Non 
fure  pajjivc  indfjfirentia  N.  m.  &  Cm.  Indiffcremia 
corpo.  um  eon)un£ta  e(t  cum  poiitivo  conatu  con(crvai|f 
di  itatum,  ad  quem  priui  de^crminata  foerunt« 

XT,  Nullum  corptis  agcre  poteft  ad  contervanddfn 
quietem  (  idem  re(i)e£tivc  dici  poteft  de  confervando 
fnotu)  ;  ergo  nulhim  corpus  vi  inertic  prceditum  eft. 
Jfv.  PU  Agerc  ad  conicrvandam  quietcm  cft  agcre  cop- 
tra  mojtum  proprium ;  (ed  nulium  corpus  agerc  poteft 
concra  mocum  proprium ;  crgo.  Ij^:  N.  A.  ad  Prob. 
D*  A,  Eft  agore  contra  motum  proprium  iiidire&e^  qua- 
tcnus  ncmpe  corpus  quie(cens  reliftit  determinationi  ad 
ipotum  aliundc  provenienci  C,  M.  Elt  agerc  direde^  (cu 
ita ,  4it  corpus  quieicens  eadcm  vi  fua ,  qua  confcrvat 
quietem,  dein  reiiftat  niotui  proprio,  poftquanr  ab  ageutc 
fpcrrawo  ad  motum  efi  deurnuntuum  N.  Mt  fic  D.  m.  & 


XIL 


V 


Lex  viriam^  i, ,.  I3S 

XII.  Tn  corporibus  motis  inertia  fiTtt  fandamen* 
tcim  morus  contiiiuari ;  iftud  vero  dici  nequtt  ;  ergo» 
Pr.  m.  Inertia  re(i(tit  motui ;  atmii,  guod  re(iiHt  morui, 
nequir  ede  fundamentum  mom?;  crgo.  .  ^.  C.  M« 
N,  in.  AdProb.  D.  M.  Inertla  refiftit  motui  alieno  ; 
h»  e,  dcterminarioni  ad  mntationem  (latus  ab  extrin(cco 
t)rovenieiui  C.  M,  motui  proprio  N.  M.  D.  m.  quod 
^efiftit  motui  tam  proprio ,  quam  alieno  ,  nequit  cfle 
fundamentum  motus  C.  mt  qw)d  moCtti  aiieno  rcfiftic» 
non  tamen  proprio  N.  m.  &Cma 

« 
Xni.  *Vis  inertis  cx  viribus  cntium  (impliciani 
non  derivatur  ;  cx  quibus  enim  ?  cxploratum  non  ha« 
bemus ,  quales  vircs  enti  (implici  corivcniant  ;  crgo. 
^.  N.  A.  Licet  ditlinae  non  agnofcamus  ,  qua  rationo 
vis  inertie  ab  entibus  (implicibus  profluat,  datur  tamcn; 
ficut  licet  difiMe oiponi  vix  qucanr  phsnomcna  ma* 
gnetis,  ae  eledricitatis,  dantur  tamen. 

XfV.  Inertia  (altcm  noii  efl;  proprietas  gcncralii 
fnateriic;  .nam  Imo  :  Proprietas  generaiis  matcri«  au- 
geri  nequit,  vel  iiiinui ;  augetur ,  vel  mii^uitur  incrtia» 
lldo  :  Proprietas  oniverfalfs  materis  in(it ,  oportct,  fin* 
gulis  partibus  materia;;  fiC  quo  plus  habetur  mafTs,  hoe 
maior  habeatur  refiftentia,  e(l  neccfTe.  I(lud  vero  fallir* 
Sxpt  enim  modica  ma(fa  reliftit  multum  :  magna  cx  ad- 
wevCo  parum ;  crgo.  Illtio  :  Propricras  generalis  om* 
nibus  corpnribus  competerc  debet ;  quis  porco  novit  » 
£  competar  inertia  ?  quis  omnia  corpora  cxpertus  fuit  ? 
|J{.  N.  A.  Ad  Prob.  D.  A.  Aogetur,  vel  minuitur  incr* 
fia  in  afio  Hdo  C.  A.  In  a£la  Imo  N.  A.  &  Cm.  Sfl^pe 
iris  inertis  ab  extraneis  ccfrporibus  aliter  etiam ,  «c  ati<« 
tcr  modificatur  (ecundum  celeritatem,  &  dirc£lionem  ; 
hinc  augetur,  vel  minuitur  a£lio  incrtia: ,  (cu  incrtia  iii 
m&n  Ildo  fumpta,  non  autem  in  a£la  Imo*  Ad  lidum 
Eadem  eft  rcfponlio.  Ad  Ifltium^^.  SafHcit  ,  quod 
cofflpccat  omnibtts  Us»  in  quibus  cxperim  cnta  inllitucrc 

14  ^       licuit. 


j 


/ 


r^S  SeTlio  T.  Caput  W. 

lieuir,  nullo  contrario  invento ;  tum  enim  valebit  prin* ' 
cipinm  indu&ionis  imperfeQa\  cruendse  verirati  aptifll* 
mum.  Hinc  Neutoui  regula  tcrtia  :  Qnalitates  corpo^ 
rum  ^  qua  innudi ,  B'  remitti  nequeunt^  qweque  corpo* 
ribus  omnihus  campetum ,  in  quihus  -experimenta  infiu 
tnere  licet  y  pro  qualitatibus  corporum  univerfomm  Jkm 
habenda ,  niii  Hllicet  ratio  pofitiva  obllet. 

« 

§.  5*  ^.  De  vi  attra3iv4  egi  alias  »  agam- 
que  deinceps«  Gravitjs  fe^ione  proxima  pe« 
culiarltm  iibi  locum  vendicabic« 

S*  57«  Henforum  <9rpirum  nomine  cenfe^ 
inus ,  (jH^  juh  ditfrminata  ali^iuo  voluminc  multum 
fnatiria  propri^  cominent.  Rarorum  nomine  ve- 
niunt^  ^ua  fub  codcm  veluminc  minHS  matcria 
propria  babcnt.  DenHtas  itaque  dici  debet  est 
corporum  difpofttio ,  {jua  fub  codctu  VQluminc  ^^^ 
Idem  applica  raritati^ 

Scboh  I,  Definitioni  hoic  rite  inteltigencl«  neceC 
iariain  ede  puto  (iRceram  ffiajfa^  ac  voluminis  cognitio* 
nem,  Majjia  corporii  dicitur  tota  quantitas  materia  ad 
ipfum  corpfis  perfiuentit^  (cu  ;  numerus  pun6lorum  cor« 
pus  aliquod  CQnltituenrium^  Voiumen  efl:  magnitud^ 
Jpatii  extima  corporis  fuperficie  comprebenjt^  ut  inclii- 
ii%  rpatiqla  vacua ,  yei  heterogencas  etiam  fubftantias 
inrra  poros  inclufas,  Aliis  voiftmen  dicitur  ipjd  corpo* 
ris  in  ofnnem  partem  ,  h,  e.  in  longum,  latum,  &  pro* 
fundum  cpfpHcatio,    R^  eadcm  dieitur,  quss  prius. 

ScbQl.  lU  Denfitaa  corporis  agnofcitur  ex  ratione 
tnateriT  ,  (ive  mafTs  acl  volumen.  Quare  fi  mafTa  qux- 
cunf|ue,  corporum  quorumcunque,  dividatur  per  vo« 
lumen  ruuin  otcunque  magnum,  vcl  parvum,  obtinebi- 
tVr  dcnfiM  ^rforsf  unius  rclati  ad  MuL      Hinc 


.  / 


tix  vtrium.  lyj 

SX  eorporii  ^denfitas  dicatur  D,  mafra  M,  volumen  V^ 
Stque  cor^oiis  B  denfitai  vocetar  d^  maf&  m^  volumen  v^ 

•rit  D.^  —  ;  atque  iterum  d  t^  -^*        Quo  pofito 

pnlcherrima  fine^  ac  atiiiffima  eruontur  theorcmati. 

M 

tUor.  L    Si  D^  m^^  erit  qaoque  M^   DF. 

V 

^  M 

Multiglicent^r  enim  gemins  lils  quantitates  ( D,  &  — ) 

ex  h^othefi  cquales  per  eandem  quantitatem  ^;    fa« 
£la  manebnnt  «qaalia  (  ^»  I.  ax,  VI.  )s  fietque  D  K=a 

MV 

——  =:  M.  QuodE.  D.  Theorena  fic  efTertur :  Mt^ 

funt  in  mHpm  €omfofia  deHfitamf$f  at  voJumiwim. 

M 
Tbeor.IL  SiDF^  Mi  «htinebitur  f^a  —  * 

"^   D 

Dividatur  enim  pars  utraque  {D  VSi  M)  per  D^i 
^uoti  manebunt  sqaaics  (  1. 1.  aic.  VI.  j  ,  6c  habebitur 

^       M 

V^  — «  h.  e.  yolumm  corforis  ohtinetur^ fi  majfa  ijus* 

dem  dividatur  per  denfltatem.     Alii  theorema  iftud  fie 
cflferunt  ;  volumna  funt  in  rattono  direda  majfarum^  V 
invcrfi  voluminum.    £roi  quidem  veritas  iila  poteft  ei^ 
"  praC  theor, 

Tleor,  liL  Si  D  :;$  -^ ,  iteramqne d^  ^;  qnb 

y     -  V 

0^ia  ad  afuaiia  Jieunt  eandem  rationem »   babebitar 

M     ** 
proportio Didsi  — .  t  — «    Terminos fteoadsK ntixh 

l 


A 


1 


138  Si^  h  CipmW. 

Aig  per  eandem  qiiantititeiTi  Vv  multiplieandoy  mtna* 
bunt  fa£la  in  eadem  ratione  (  §•  !•  a|C.  VII.  Schol )  ; 

fictque  Did  z:  — —  ;  — —  =s  MvimV.  h,  c.  ieii* 

r  t; 

foatet  ftint  in  rotiofic^eompqfitt  tx  direfta  maffarum^  ST 
inverfa  voluminum. 

Theor.  IV.  Si  Af  =:  m,  crit  D :  J  =:  » tV.    Qom       ^ 
enim  (  per  Theor.  prae.  )  D  tdn^  M  v:  mV\  6\\'\^vg 
lecundx  rarionis  terminis  per  M  z::  m  (  quod  faiva  ra* 
tionuCTi  sqnalitatc  ficri  pofie  dorct  ^*  i.ax.  VII.  Schbl.)    '     '' 

Mv      mf^ 

liabcbitur  Dt  d^  •—  :  ;   eliminatisquc  fra* 

'M  m 
fiionibus  crit  D  :  dzz  v  •-  V.  \ue.  Jt  majft  fnerint  <f. 
^aies(  c.c.  liira  argcnti,  &  lihra  apri)  ernnt  dett/ttates 
reciproce  nt  volumina  ,  fivc  •  hoc  majdr  erit  deniitas  ^ 
qno  mrHUS  voiumcii;  hoc  minor  dcniicaSy  quo  majut 
Tolumen. 

Tbeor.V.  Si  F=:  v,  eritZ>?^i=-  M:m.  Nam 
cft  (p^r  ante  di^a)  D  :  d  z::  Mv  :  m  V.  Ja m  fi  termi. 
Hi  cjosdcm  rationts  (  fecu  A^  fcllicer  )  per  eandcm 
quanritarcm  divtdantnr,  quoti  manebunt  in  cadcm  ratio* 
ne  ^§.  I.  ax.  Vll.Scbol.  )  •  Dividcndo  pcr  J^^s  v, 
Mif      mV 

€tt  Did  :=i  :  —  =3  ilf :  i^,     (^mrt  fi volumi^ 

•V  V 

IM  eorporum  ^equalia  funt  ^  erunt  denfitaus  iu  ratione  di*       , 
reQa  majjarum. 

§.  53»  Ut  vidco,  denfitas  eorporum  repe-' 
ttnda  eft  a  vicinicate  particularum  minima-» 
rum  ca  componentium.  Raritas  ex  adverfo  a  ^ 
majore  eariindem  molccuiarum  minimarum 
diftancia.  Yeritas  Imq  iponce  fluic  ex  data 
definitione^ 

Oraff* 


CoroJl.  Minm  iuiqae  forofa  efle  debent  eorpora 
^enfi^  qaam  rara. 

§.  5<^.  A  varu  denfieete,  &  rarieate  cor^ 
porum  pendet  varietas  gravitatU  Jpeeifica^  Cor» 
pora  quo  dcnfiora^  hocjpecificc  graviora.  Gra- 
Titatis  iftius  theoriam  prius  quam  expono^  aue 
Terius  atcingo ,  debita  ejus  notio  animo  in« 
formanda  eft,    Permagni  refert  eam  noviiTe* 

$•  60.  Triplicem  gravitatem  diftinguunt 
Phylici  fccundum  nomen  :  ahfolutam ,  re/pelii'^ 
vam  I  &  fpocificam.  Re  vera  admictunt  qua« 
drupltcem  ,  nam  abfoluu  gravitatis  nomen  ge- 
mino  diverfb  fignificatu  murpant :  primum, 
ut  opponitur  graviti^  fpicific^ ,  tum  ut  rcfpt^ 
fiiva^ 

S%  61.  Graviutt  ahfilutd  (ut  opponiturj^r«i 
dfica  )  eft  Summa  omnium  particularum  gravium 
in  corpore  aliguo  contentarum.  Aliter  pon^ 
dus  dicitur.  Gravitat  fpecifica  corporum  eft 
fondus  illud^ijuod  fub  certo  volununo  torpora  ch» 
tinenJt ;  five :  eft  pondur  relatum  ad  valumen  ^ 
darius  :  divijum  per  volumen. 

ScboL  AnAlyticc  gravitas  abfobisa  dicitur  G;  gra» 
G 
vitas  Jpecifica  —  •    Siqac  plara  corpora  e.  ef,  A  O^  B 

V 

conferentur,  dicetur  gravitts  <ii|/o/»fa  corporis /tf  s:s  G\ 
G 

ffecifiea  —  .    GmtNs  ahfdms  corpoijs  Bxa  gi  Jft» 


i^6  icSht  CifutiV. 

g  ^      S 

tifica  =:   —  .     Qatre  yf  <  £  o   —  :  —  •     JEftalh 

^m  Md  aqualia  Ifc» 

G  G 

Cor6JLL  Si/#=3  — ,fict//r=!  G,  &  F=!  —i 

V  A 

,  tles  eodem  modo  probanir,  ut  fupra  diAum  td  matet» 
riam  de  deufitc^tt^ 

CoroU.  11.   Facile  ctiam  crultur  :  gravitatem  atji^ 
htam  corforif  cujusatuqya  ejfe  ut  wajam  ejusda/u  '  ^ 

^.62.  GravitMt  shfiluta  (  iit  opponituf 
rcfpcSiVa)  e(l »  qua  grave  tibcrc  in  mcdio  non 
rcfificnte  defcendit ;  e.  c.  cum  globus  aureus  ^ 
vel  pliimula.  ex  quapiam  attitudine  delabun- 
tur  in  vacuo  Boylcano.  Gravitas  rcfpeSiva  ed-^  "^ 
^qua  grave  dcfcendit  paru  virium  aliqua  in 
nlium  effcflu^  impcnfa,  puta  ^  in  prcjfioncm  objld^ 
culi^  e«c«  cum  vas  volvitur  per  planum  incli* 
natum ;  auc  in  fupcrandam  mcdii  rcjtjlcntiam  p 
ut  ii  corpus  in  aere  movecur. 

f .  63.  Theo^ema  priiiceps  de  gravitate 
ipecifica  tic  habet  :  Gravitatcs  fpccifica  duorum 
guorumvis  corporum  (  quas  A^  &  B  vocabo)  funt 
in  rmonc  tompojita  cx  dircctd  pohdcrum^  feu  gra- 
Yitatum  'abiolutarum  f  (f  invcrfa  voluminumm 
v^^  G      g 

Nam  (  per  §•  6u  SchoL )  if :  JB  =:  —  :  —  t 

^     V-^    V 
Ergo :  AtB^st  Gvtg^.    Demonilratidneni 
pulio  negotio  erud  ex  §•  $7.  Theor.  lil. 


Ltxvhrtum,  H* 

CtroJL  I.  Qaui.grawtatet  fptcifica  iuertm  eorpt. 
rum  id*m  pcudtts  bahmtiiim  fimt  iuratiofU  reftproc* 
vorumimm.  Si  enim  JtB  :=  Q  «  '.J  ^  (  P« i 
pr«r.  )  dividendo  termino»  Mtionii  fecand*  p«r 
Gs^,  fiet  AtB  :£   vt  F.Q.E.D. 

Corott.  it    Gravitatet  fpecifica  duorunt  corporum 
idet»  volutneti  babentium  fnnt  in  ratioue  direaa  poudf 
rttm  ,  feu  gtavitatum  ahfolutanim.     Nam  aflumpta  ite- 
rum  proportione  .  ji  •  d  —    \j^  .  «  '  »         ^     ,  . 
vifione  terniinorum  rationis  fecundse  yec  K  =S  « ,  odop 

oebitur  Ax  B  ^   G'g'  0:^'^' 

CoroU.  III.  Gravitates  Jpecific*  daoruia  torporum 
tmt  ut  denfitatei.     Nam  GraviuK  abftUm  ex.  dcfinmo. 

G        M  ^ 

ne  fat  =   maff» ;  «rgo  —  =3  —  (  i  «•  ««•  5- )  « 

vcro—  s:   D  (^.  57- Sch?  II.  ^i^reo*^*"''^^^  *^ 

Pprro,  quia  ^:  S  a  ~*  — (S.^i.Schol,),  fiiaafub- 

ftitOtionc  fict  : -^  J  fl  =:   D:rf.    ^.  £  ©• 

Groff.  IK  Gravitates  ahfiluta  duQrum  corporum . 
ybnf  f «  rfl//o;if  compofita  'Ooluminum,  0"  gravitamm  fpe^ 
tificarum.  Eriam  vcritas  ifta  fluit  ex  principc  Theorc 
njre,  quoCipra  eviaumefts  legiiiiTiain  cfle  propor* 
tionem  ;  At  B  ^  Gv.  gV,  quarc  cum  faaum  mc^ 
iiorom  «qualc  fit  fado  extremorum  ,  obrinebitur  1 
y#^  r  C3  fi  G  ir.  Gemina  h*c  fatla  «qaalia  (olvci*. 
do  in  proportioncm  faaores  rcciprocando  fiet  %  G  :  g 
^   jW^:  Bv.  Q.E.D, 

Scbol.  Gravitates  abfihta  cxplorantur  ponderibut 
fUlSO  fiodiO»  ;  •fwifjwm,  Wr*,  htbwt  &c  ,   hjt 


\ 
\ 


/ 


14«  SeBhP.  CaputW^ 

emm  paitim  inetimur  corporum  pondcra*  Speclfic^ 
innotcfcunt ,  (i  gravitaccs  abfolut^ ,  feu  ppndcra  div^ 
dantur  pcr  volumen  bpe  /lereometria  invcnlcndum* 

§•  tf  4.  MoUitiei ,  £^  duritics  hoc  loco  exa- 
ininanda  veniunt.  Duta  dicimus  ,  qu«  im* 
prellioni  fadac  ad  mutandam  figuram  non  ce«  ^ 
dunc»  fed  eidem  plurimum  refidunt;  moUia^ 
quae  impreffioni  tali  facile  cedunt ,  neque  in« 
dependenter  ab  adione  corporis  exrranei  fi«  { 
guram  refumunt.  £.  C»  durus  cft  adamas  , 
siam  frequentibus  malleotum  i^ibus  figuram 
non,  mtitat.  Mollis  eft  targilU  >  facile  enim  cQi« 
que  irnpredioni  cedit ,  neque  yirtute  propria 
nguram  priorem  refumit,  C^a^^  duritiis 
elt  afft&io  corporum ,  ^ua  imprifficni  faffa  ad  mu^ 
tandam  figur/tm  notk  f$c%U  cedunt.  MoUitia  t& 
^eBio  corporum^  qua  &c. 

SeboU  Cerpora  petfeSe  dur»  vtx  dari  puto  \  om« 
nia  cnim  corpora  ((altem  qu2  hadcnus  innotucrant )  iftu^ 
ac  pcrcuflioiTe  iiguram  miitant.  Gbnjicio  iftud  ab  ex« 
pcrientia^  qust  docct :  globos  vulgo  duriflimos,  ut 
marmorcoS)  vitrcos  ^c%  pofl;  confli^uih  a  (e  fe  divelli  ; 
quod  tamcn  ncutiqiiam  futurum  efTe  >  ii  fyh^vk  tllat 
mnnim  durse  (int ,  patebit  cx  Legibus  conflifluum  ini« 
fi^  recitandis*  .^^ccdunt  tamen  ad  corpora  perfe&e 
dura  globi  ex  argilla  non  nimis  cxiiccata  fabreffl^li. 
Ccrtc,  Mariotto  tcftc,  leges  mocus  corporum.p^i^fle 
ehromtfi  hisce  in  giobis  ad  ftnfum  obfervantun 

§.  6y*  MoUities  corpoYum  e^piicatuf  pef 
(requentiam  limitum  cbha^fionis  in  diftanttis, 
femper  adbuG  oiiQimis»  .  Oporcec  tamen  limi« 

4  tes 


Lix  virium.  14% 

tti  coharfioni^  ntn  ^dmodum  e/Te  vaUJjs.    Qvio 
paifto  fiet ,    ut  corpora  facil^  &   frequenter  - 
'  cedant  impreflioni  fs(£tx  »  neque  vi  ulla  pro» 

f)ria  (e  fe  in  priorcm  figuram  reftituanr;  mo- 
ecula?  enim  minimarde  locodimotae  facile  ad 
\       proximos  (  qui  viclniffimi  ponuntur  )  cohx- 
L      iionis   iimites   deferentur  ,   &  cohquiefcent» 
Indc  jam  facilis  explicacu  erit  duritui^ 

^,  66.  FragiliUs  audit  u  affc^ie  corporum  f 
^a  fdciU  partes  a  vidnarum  CGnta^u  phyfico  fic 
avtUuntur ,  ut  alid^  tfuibus  adbarefcant ,  non  fi^co* 
dant.  Oritur  fragilitas  a  limittbus  cohxjSonit 
-ddmodum  paucisi  non  omninb  validis.  Si 
fdttti  erunt  »opartes  adhibita  vi  extrinfcca  (ic 
ab  invicem  divellcntur,  ut  alix,  quibusQd<«  . 
hatrefcant ,  non  fuccedant.  Si^M€  non  admo'» 
dum  vdlidi^  facile  fic  divellentur. 

§.  6>J^  DuSilitas  fragilitati  opponitur» 
eftque  ea  corporum  difpofitio ,  ^ua  parte  una  lu^ 
bricando  dimota  facile  altcra  fuccedit  ,  priori^aa 
atdharct*  fendet  illa  a.  magnitudine  arcuum 
attrahentium  ;  (i  enim  pundum  de  limito 
cohaefionis  dimotum  vi  extrinfeca  dcferetur 
{ub  arcus  valide  attrahentes  facile  pun(ftuni 
.  alterum  fuccedet  ^  priorique  adhatrebic  (  $• 

36.Theor.  VI.  )• 

• 

Scbol  L  Scberffirve  ait  repetenclam  cflc  dudiHtaF 
tctn  partim  ab  attradione  tnutua  ,  partim  ex  admiftf* 
onc  Haidi ;  neque  tan?!!  inodos  alios  ,  quibus  (imi* 
li»  ifivftioia  corpoia  inducatait,  c&clttdcndos  cenfe^  . 


144  &3iol  CAputlV. 

SchoL  IL  Qnm  de  duailitate  di£U  (unt  ^  edatn  in 
PidBeaiilmtem  convenire  deDent^ 

^.  6^*   JJperitai  eft  in«qualis  dirpofitio 

Sartium  extimam  fuperficiem  corporis  con- 
ituentium,  ac  p^lo  durioruin  >  q.uarun)  aliae 
prominent  ultra  alias  ,  alias  vero  retro  ce** 
dunt.  GlabriHes^Gve  Lavitas  eft  ^equalis  difpo* 
fitio  partium,  extimam  ruperficiem  compo-* 
nentium. 

Schh  Utcanque  politfls  corpbrum  fiiperficief^ 
fimper  tamen  aliqiiatenus  tfperas  eHe  innuit  {•  48« 
Sqhol.  II,  Opp.  IIL 

i 

§.  69.  Ex  afperitate  corpor^im  nafcitur 
gffriSIus  ftu  friciio.  Eft  autem  fricaio  refiften- 
tU  (Iiperficierum  fuperanda  a  Corpore^  quo4 
ita  movetur  fuper  aliud,  ut  amborum  fuperr 
ficies  fe  mutuo  radant.  Refiftentia  illa  in 
inceflu  corporis  unius  /uper  alterum  haberi 
omnino  deber.  Qum  enim  corpora  omnia 
iuperficie  afpera  fnftruda  fint,  prominentix 
unius  in  alterius  .cavitates  1  ac  fovtolas  fe  C9 
infinuent »  eft  necefle« 

Scbol'  J*  Quantitatem  afFrictus  metimur^  paflim 
non^  tam  (iiperficierum  fnagnitudine ,  quam  pondere  ac 
frejpofie  plani  alicuius  mobilis  fiiper  plano  alio  inceden- 
tis.  II.  Ubi  raagnitudinis  fuperficicrum  ratio  habetury 
]itndet  afFridus  a  duritie  particularum  promiuentium, 
Hsc  vero  cum  penes  diver(a  corpora  varia  (it ,  conftanf 
fri£lionis  ratio  baberi  nequaquam  poteft.  Mu(cbenr 
bxaeckias  0ai.penmfin(qrHm  ope  evinck ;  q[uanritatem  a^ 

friaua 


/  -.' 


I 

M6tixs  £tpt  ftquire  |  preffionis ;    zioDfiQnqtiain  l^^ 

I ,  ^ ;  Don  caro  «it  minoretn  obtinere  frifiionem.  III» 
pendet  etiem  quatititas  fridioni^  tf  dher/A  Jpecie  fkm* 
rum  (upcr  fe  fe  incedentium ;  longo  enim  ttiu  machina* 
tum  fabricatoribt}»  Compertum  cft  i  corpora  beteroge» 
nca  minorem  afFridum  pati »  quam  hombgenca»  Cer* 
te  experientia  teflc  longe  ma)cr  afFriaus  eft  chalybit 
(upra  chalybem  ^  qoam  (apra  (tannum)  ant  orichalcum» 
Hinc  in  maciittnis  plerisque  aitfes  rotarum  e  chalybe  for** 
inati  orichah^  incumbtmt» 

SM.  tL  Rtmedia  fri£lionis  ad  quinque  dapitt 

revocatitur  S  t»  Juvat  ruperficres  corporum  expoliviflilk 

II.  roinuifle  \  quare  axicuU  tqtis  infdrendi)  quo  minorii 
diametri  ^  hoe  meliores.  IIL  Corpora  oleoft  ^  aut  pift' 
guia  cavitatibus  expitndis  maKime  idonea  iti&ifuiirtt 
iV«  Meterc^en^  corpora  coRjunki(&»  V.  Motufm  ra* 
dentefn  ^  five  kbricatiotnt  in  motum  ro&ttonia  immn« 
taire»    Hine  pri^grandia  I«pe  otttra  corra  dtvehuntur» 

'  ^;  7d.  ElsftUitas  illa  dicitur  aftSiio  ^  au4 
iorp^a  ftexa  i  Un/k  ^  aut  cmpriffa  priftina  fi^u* 
if^  fi  fe  reftituunt^ 

Scbiit,  C<$rpora  omnia  in  (e  etaftic^  efle  con^ciont 
oonnuili  ex  eo  ,  quod  corpora  nnlla  perfede  dura  fint» 
Oari  tamen  corpora  ad  (enfum  non  tlaliica  evincitur  t 
ihoUibuS)  mz  ob  frequentiafn  y  acoidnitatetfKWmixxLta 
cohtSonis  ur  le  in  priorem  fignram  non  reftituunt* 

f  «  71.  Nafdtur  $lafticita$  cx  tocattdne  pun^ 
Sorum  in  limitibui  cobaftonis  >  circa  qu6S  bini  arcui 
mrinqui  ftoximi  funt  fatis  ampli  ^  at^uo  ad  majui 
intervaUum  fi  fi  ixporrigentes.    Nam  polita  Io« 

cationc  paaftoriva  io  diaii  limitibus  partei 


-y 


14$  SeSlU  Tk  Oput  ly. 

de  loco  ditnots  priftinam  figuratn  rerufnuilt^ 
&  non  pofita  non^refumunc;  (ed  quo  poGc6 
partes  in  prior^m  figuram  Ce  fe  refiituunr,  8c 
iion  ponto  non  (e  reftituunt,  tn  eo  ftatuenda 
eft  eiaftidras ;  ergo.  Pr.  M.  Si  pd/ta  hac  fo- 
iatione  punHorum^  ^  mplitudinc  arcuum  pkri 
tina  urgeatur  verfus  alcerani ,  incidet  tub  ar*, 
cum  repulfivum ;  quare  ceftance  vi  urgence^ 
&  comprimence  repellecur ,  &  repul&  defe* 
retur  ad  priorem  coha^fionis  limicem,  peraAis* 
^ue  circa  iilum  ofciliacionibus  complaribus 
in  eodem  perfiftet,  Sique  pars  alcera  TepaW 
retur  ab  alcera^  incidec  fub  arcum  attrahen« 
tem ;  proindeque  cefTante  vt  extrinfeca  at- 
trahetur  ,  &  accrada  denuo  ad  priftinum 
cohaefionis  limitem  revertetur ;  (emper  ergo 
corpus  five  comprefliim^  five  tenfiim  t  ft*» 
flexum  figuram  amifiTam  recuperabit» 

icbot.  1.  In  exetnplo  fic  cannt  elaftica ,  qu^  (i  prc» 
lienHs  anibobus  extremis ,  propiusque  acl  (e  £e  addu6lia 
infleclatur,  iibi  relida  priorem  figuram  refumit.  Phx* 
Mmenon  in  theoria  nT)ftra  facilem  liabet  explicacum^; , 
icilicet  t  quantumvis  ex  parte  couvexa  multum  pun£ia 
t  {e  invicem  recedant ,  manenc  tamen  fub  arcu  attra* 
bente^  qui  egregie  amplus  efleponitur^  ergo  cefianta 
vi  infie£lente  fe  attrahent.  ado.  Licec  ex  parte  cpn* 
cava  multum  pun£la  ad  &  i[e  adigantur,  manent  tametl , 
fub  arcu  repellente ;  iterum  ergo  cellanie  vi  extranea 
ic  repcllenh  Atqui  Vcrb  ii  iftiii  (e  attrabufrit,  illa  ra-^ 
«ellunty  canna  priorej^  figuram  refumerc  debet ;  crgo* 

Scbol.  XI  Ofcillationej  illas ,  qu*  fiunt  a  punftiSf 
r^verrcntibus  ftd  prioremlimitem  cohsfionts,  indicat 
fonus ,  qui  fcp*  exaudinir,  «um  corpoila  tlaftica  mi& 
Um  fig«ram  ^«ecDfcraot. 


I 


Lex  virkim.  '47        < 

^,  ^2.  Cdufa  elajlicitatfs  in  mimrijjus  dif 
^antiis ,  fve  ,in  corporibuh  tomfrtjjis  efi  vis  repd» 
Ifm  )  in  difiintiis^  majoribus  y  h.  r.  in  corporibut 
tenfis  vis  attrabens  ;  in  fiexis  partim  vis  attra^ 
Riva  ,  partim  rtpulfiva.  Probatlo  defumiturex 
$•  prioru 

CoroU.  I.     J^uare  caHifaphanomemrnm  elaflicitatif 
ii^n  efl  nna  attra^io  ,  ut  voiunt  Neiitoniani ;   quamvit 
«nim  plurimum  ci  tribiwndtim  fit  in  torporibus  ten^ 
fis ,  ctim  ca  prioi:!  figuri  rcftirtjUTitttr^  at  quid  in  cof- 
poribus  compreffis  in  acceptis  ei  fercndum,  dum  iftf 
pontionem   priftinam    refumunt  ,    phne   non   video, 
]?trvide6  immo  imminutis  pcr  compredionem  dlftan* 
^is  majorem  vim  attraSivam  excri  debcrc  (perlcges 
Ncotoni);  ideoquc  corpora  comprefla  nmrquam  figu-* 
tx  priori  rcftitucnda  c^e.     Sal  neque  fi  Argus  lim , ' 
ridere  (pcro,  quomodo  corpora  prius  fiexa  vi  miius 
tfttradfonis  priorcm  figuram  induanr.    Sane,  fic.  c,  la* 
mina  claftica  inHedatur  y  augetltut  diftantide  moFeoilai- 
Am  c  parte  cbtivcxa,  minuunmr  c  concara.     Sequituc 
Ihinni  attra£Wonem  c  partc  convex-a ,  augcri  c  concava, 
Sed  &  illud  cortfeqnirur  i  hoc  pafto  adeo  figtirae  rcfti- 
r^itioticm  ficri  non  pofle,  ut  ob  auftam  cx  partecon-' 
«avaattradioncm  figura  iamin^  ftex«  immutata.conier»' 
Vari  dcbcat* 
*  ■ 

.4.      Ckrofi.  It:    Caufi  ^k/Hditatir  ^e  ne^iit  anr  iutra  ' 
Horporum  porot  i^aercepm^  iisqtie  tomprejjis  tchnprejfus  ^ , 
4SC  fahinde  ceffante  vi  tontprimeme  fe  fe  etipandere  nitens* 
S\t  cnitn^  tiifi  vehemcnter  fatl(rr,  ibitur  in  infinitum« 
^uid,  quod  pli«nom«i3ia  ciafticittttis  habcntur  «liafn.in^ 

TfAOlO  «  . 

Cotot  Itt     i^^Ui  i^tr  mipt  ehfiicitatu  torpo» 
tum  did  fos^    Alietttm  ctitm  «  icorporibaft^Aluft  aA 


N 


14$  SiShT.  CapalV. 

ctherem  transfertur  quarftio,  non  /blvitur.  ^AJdunt 
alti :  sther  rubtilifliinus  poros  omneS'  penetrtre  capait 
claberetur  inrerea  ,  dum  f  orpus  compr^mitur  ;  atqu9 
fiibUta  comprefltone  irrueret  denuo.  j^wtrunt  i  eit 
una  duntaxat  parte,  an  exomni  irrueret  ?  Si  tmum  t 
cur  canoa  huc  6ve ,  five  illuc  infiexa  ligoram  rerumirfL 
ii  alterum  :  quomodo  iigura  priftina  recuperatur ,  cua| 
atther  parte  una  sque  premat,  ac  altera  ? 

■'  .-'^-    ..   ■  '    '  ' 

Carjfl.  IV.  Emm  iguif  intra  poros  corporum  bkk 
titanSy  vique  repulfiva  praditm  caufa  tlafticitam  mn  efi^ 
Multis  enim  corporibus  ignis  ela(lidtatein  omnem  adi* 
fliit.  / 

ScboU  Quam  nuUa  fint  adverfiriorum  arguitietiti^ 
breviter  exponam  :  Dicunt  h  In  theoria.  hac  expiicar^ 
neqneunt  pbsnomena  elaflicitatis ;  ergo.  Pr.  A.  £«t 
plicari  nequit  I. :  qoi  fiat,  ut  in  corporibiis  diverfis  di» 
verfi  fint  clafl:icitatis  gradus«  IL  qua  ratione  ^orpori«i 
bus  quibusdflm  antea  parnm  elaflicis  infignis  communi^ 
cetut  elafticitas,  III.  Cur  corporum  q^orundam  efa^ 
fticitjatem  minuat  humor,  aliorum  calor  ?  IV.Cuc 
ignis  ope  jam  major  ,j$m  minor  concilietor  vis  elaftii^ 
ca  ?  V.  Ouomodo  corpora  qu^dam  diuturrtiore  fitot 
ciafticitatem  exuant  ?  ^.  N-  A.  Ad  Prob.  L  a^o  a. 
aiyerfi  elafticitatis  gradus  a  varietaie  limitum  ,  &.ac)ft 
cuum  utrinque  vicinorum  funt  repetendi»  Ad  lU 
Conciliatur  elafticitas  five  bnmoria  Juperflui  expulfioue^ 
Swefluidi  cuju$piam  iHduSime^  e.  c.  olei  ;  tum  eliim  o> 
molecula»  aliter  difiantes  novam  virium  compofitionen» 
^iriri  necefli  eft.  Pli^nomenorum  llltii ,  &  IVti  i<atia 
cflr,  quod  ignis  0  nam  quod  bumoretift  attinec ,  eat  jam 
diaisaluinde  refellitnr)  vehemjBOti  mok«ularttm  eooN 
snotionc,  ac  perturbatione  novam  generet  virium  coiiv 
iugationem,  narticulasque  alias  ad  betie  validos ,  alias  ad 
t^midor  cobafioi^,  limtii  adduGat,  nonnuUoa  eiiam  ai 

Umim  fm  calMmi^    Stdeoi  mok  Yitiusi  c«mp«ii« 

^'  ttOttt< 


iibiie  neft  tttdem  victnoram  arcattm  emf>titade  obii« 
Heri  poteft.,  Ad  V,  car  corpore  fito  eUfticitatem  t* 
mittant^  in  aio(t  eft,  qabd  ^ioM  caloru ,  &  /rigeHf  , 
itemque  panium.mnnulUrum  tranffirMimtt^  atqoe  ali^ 
rtim  iuduBione  novt  ociacor  particiilarum  diipofitio^  & 
Tkiiun  cdn;onfiio. 

Inqumnt  IL  Si  cao(a  daftibitatif  dicator  via  ntttt/» 
fKra»  t)c  repolfiva  :  magia  elaftica  efle  oponec ,  qnc 
inajore  vi  attrahendi  poilent,  ac  repeliendi ;  non  aotem 
Cxpt  magia  elaftlca;  ergo.  Pr.m»  Majore  viattraben- 
di  poilet  magnes»  qoaui  marmor,  aot  ebor,  nec  tamea 
magnes  efl;  magis  elafticos  ;  ergo*  Ijt-  T.  M;  non 
cnim  ab  aurubinu  folum  vij  V  reptttfinee  pendet  elafti« 
Citas,  fed  fimal  ah  i^Htudifie  arcuum^  D.  m.  Non 
'  amtem  {iint  magis  elaftica ,  deficiente  rcilicet  ampli.udi* 
ne  arcmm  otrinqtie  vicinorom  C»  m.  Habita  bac  am* 
pHtodine  N.  m.  &  Cm.  Ad  Prob.  D.  A.  majore  vi  au 
tradiva  pollet  magnes  refpeSu  corporum  extraneorum 
C.  A*  relate  ad  moleculas ,  e  qoibos  componitor  Subd.  * 
Sosit  tamen  molecolse  magnetis  locats  in  iis  limitibos  , 
circa  quos  bini  arcos  proximi  non  fimt  *cqoc  ampU 
C.  A.  funt  «qoe  ampii  N.  A«  &  Cm« 

IIL  Sola  attradio  eft  caoA  elafticitatis  ;  proindc 
clafticitas  non  fimol  pendet  a  repolfione.  Pr.  A»  fdem 
iliod  eft  caofii  elafticitatis ,  q«od  firms ,  ac  ftabilis  co- 
liaefionis;  fed  attradio  eft  caofii  firmar,  ac  ftabilis  co- 
fjisefionis ;  ergo*  ^*  N.  A.  Ad  Prob.  T«  M.  Plt^s 
enim  dieit  elafticitas,  qoam  cohsfio*  Nafcitur  cohsfio 
ejT  fola  locatiofte  pundorum  in  limitih/t  cohafionit  i 
clafticitas  flmtil  ix  amplitudine  arcunm  otrinqoe  vicino- 
rom.  D.  m.  attra£kip  ;un^a>epolfioni  caola  eft  cohc- 
fionis  C  m.  Una  attradio  N.  m,  &  Cm.  Per  eehc« 
fionem  r^fiftont  corpora  tam  foi  diftra£Uoni|  qoant 
tomprei&oni.  Diftraaioni .  qoldem  reiiftont  per  vin$ 
mtrakeitmm ;  at  eemprefltoni  par  ripeUeuMm. 

K  j  .  IV. 


*•  IK  jKthtt  frimens  in  pcuros  Goppdfiifn  twS\  eft^ 
car  preHa  corpora  figuram  priorcm  refumant  ;  crgo 
mthft  <M|u&  cfi  cUfticitatis.  Pr-A'  ^ther  irrucns  di. 
]atat  valumcn  carportuQ ,  plane  ficut  aer  cxpandlt  v$R^ 
«aui ,  igViis  merailmn- ,  aqua'  fpongum  >  hamincs,  ligna 
&c.  i  crgo«  15*.  N.  A.  Precario  cmiix  rv^mittiF  $• 
thcr  illcv  Ad  Prob.  Tt  A^  'Nam  cum  poros  corporum 
faciliimc  pervadat ,  dilata^ia  vobmink  hatid  abtincri 
potcft.  N.  Cmt  /Ethcr  enim  certa  alic^ua  dirc£liont 
irrueret ,  vcl  amni  cx  pa^te  ?  Si  dire^imt  iumaxat 
mna:  quid  oft,  quad  corpora  quaquaverfum  prefla  , 
«mflexa,  mutataqiie  (ita  priore  in  o^ppofitam  %arani 
limifiam  rccuiperant  ?  &'  omni  ex  fo^rtf  (  qooil  quU 
«lems  non  fiK^iie  cancedent  advcrfarii ,  e  quarum  rcnten>t 
tia,  licet  amnem  in  partem  squabilitcr  prcma^  sthcr^ 
tamen  reliquorum  fluidorum  mitar  detcrminata  quadani 
direclione  fluit )  num  explicari  poterir  elaftieitas  cor* 

Jorum  flexorum  ?  Non  pato.  Vidcatu*  §.  pr«C:  Cor, 
IL  Dcinde;  acccrfantUr  0rpojra  teufa;  quid  rera 
pencs  ifta ,  cum  priori  figurk  rcftituuntur  *  .ofEcii  h^ 
|>eat  aerhcr ,  nqn  aHoquor, 

K  Corpora  fleaa  porott  liabent  CoHkott.  ^  Pdrti 
convexa  latiorcs ,  o;pncava  five  inceriori  anguftiores  i 
quootrca  majore  copia  affluit  stficr  (iibtiiiflimusi  part^ 
latiore.  Dumque  pcr  angnftiorem  corparum  flexoruf9 
partem  efHuit,  in  hitcra  coar^atoru.m  pororam  impin^ 
gere ,  parres  propius  ad  (e  addu^as  cxpanderc  ,  priftii 
Bumque  molecuiarum  (itum  roftitaerc  dcbet ;  rc(te  igi« 
tur  ab  stherc  repetitur  elafticitas.  CoHfirvs^afHr,  Aque 
per  anguftiorcm  alv<cum  dccurrcns  maiori  celcritate  fcr« 
tur,  impetomque  majorem  exerit  in  ripsts  f^ard^ntes ; 
crgo  a  pari,  Ije.  Si  millies  in  fappcti^  vocctur  a?ther» 
nontamcn  aUud  inde  conficitar ,  quan:)  mere  per  ^i» 
Jkfu  figuroB  amiflc  reftitutionctn  confcqai ,  (i  vidcUcet 
latiore^  corporam  flexoram  pori  stheri  data  quapiafo 

dif 9^ouc  iiapnci  gbvcf tanWt     f  K  vcrp  #  c waa  vn 


y 


I 


Itx  viriumt  151 

eontrariam  fltum  infiefiatQr  s  nam,  orp^  prodcrit  quid^ 
^uam  iters^trpr^Bclari  iliius  «tbcris  invocatio  ^ 

§.  73.  ReJkxU  habetqr,  dum  corpora  per 
mediuni  aeterminats  denfitatis  (aut  per  va« 
cuum  )  progrc4i^ntia  2  .&  ^d  gon(inium,me-^ 
^u  d^nfioris  delata  ia  medium  anterius  re^ 
grediuntttf,  Dum  vero  corpora  in .  mota 
conftituta  e  medio  uno  in  aliud  diver^  den-» 
fitatis  deferantur,  mutataque  diredione  ab 
inito  (ramite  aUcjuantum  recedum|  habetur 
tcfraSlio. 

Scboh  De  caaGi  reflcx}onis,^pn  illaqiiidem  immcf» 
diata  (  qusB  indubitate  ell:  vis  motrix)  fed  de  mediataj^ 
«c  dererminante ,  ut  corpus  vh  direftioni  fuae  oppofitf 
rcgrediatur,qasrunt  Pbilofbphi,     Quapilioni  (a(ii^aci2ifn« 

^.  74«  Q^ufi  rtficxionn  eft  plajiicitat  corpm$ 
prcujp^  Pr,  PoOta  elaftigitate  corporis  per« 
cuifi  determinatur ,  &  non  pofita  non  deter^ 
niinatur  corpus  impingens  ad  motum  refle<- 
xuni  ([  nam  corpus  percuifrum  nicitnr  ela(lici« 
t^te  fua  priorerh  figaram  refumere ;  nequit 
aut^m  .r^fum^rc ,  nift  impingcns  a^  fe  remo-# 
yeat»  &*  determinet  a4  reil^xionpii)  )  \  Sed 
qiiQ  pofito  &c  j  ergo, 

CoroU^  Ela/licitai  ccrpom  pircutiemis  ^aufa  refle^  ' 
9ciatif  tion  e/i  ;^  percutiens  enim  elaflicitate  fua,  ac  ni£ii 
fig^riim  Amiflam  rccop^andi  nrgetur  diredione  reflen 
sc^oni  oppofita ;  non  ergo  vi  elajlieitatis  fus  deterrnj^v 
tur  ad  motum  reflexutn.  'Sunt  tamen,  qui  impingentil 
el4ftici(atem  CQnfcrre  dicatit  fd  reficxioncm  proptercai 

K  4  «  4^04 


I$ft  ScSikl  CafiitlV^ 

qaod  minos  tlAftic«  miniic  rcfledantur ,  nihilqiie  a4 
finfiim  eldftict  mbil  itidcm  refledaotQrf  j1gi^$$or  iU 
l$s ;  (ic  tamen,  at  reflcxionem  pendere  piitem.tb  eiafti*^ 
citate  impingentis,  ^^a  tnera  coiulMatie  ^  non  ceu  ven^ 
Wifa»  Condim^  inqqgm ,  efi  \  nam  fi  impingcnt  in(i» 
gnicer  raolle  fuerit ,  cui  niiila  «d  (enfum  infit  eisfiici^ 
tiis,  Qbftaculum  vix  eomprimet;  cnmque  moiya  ple? 
rumque  majorc  vi  CQhsliva  poUeant,  adhs^rebit  potiuf. 
Sique  infigniter  durum  erir ,  atque  iteram  (enfibiii  ela« 
fitcitate  dcftitutum^  fuperabitur  vis  daftica  corpori» 
comprefiit  Proinde  nuUo  cafuum  di£toram  reflexid 
habert  poterit.  O^fy  non  ift^  quia  Qon  determina(  «4 
4ire£tionem  motui  priori  oppofltam, 

S^boU  Nihil  profllKim  t j}ver&rii  oggerentes  1. 1  Si 
eUfticitas  dicttur  cauft  motus  reflcs^i »  muitiplicert  n» 
ves;  quod  dbfurdam,  j^t,  Multiplicimtur  cum  ratione 
iiiificiente  C«  A*  (ine  iUa  N«  A»  &  Cm«  Ratio  fuflicienii 
ndftruendc  hoc  ioco  eiafticttatis  ceq  caufie  eft  in  oppo* 
fita  dirediont  corpprii  rcflesci ,  ad  quahi  cum  impin^ 
ffcni  (emet  dctermiuare  nequeat,  a  cauGi  extranca  deter«« 
minari  eget«    Qu^  verp  Ul9|  fi  non  eiafticitas  corporit 

peren(&? 

« 
II,  Sine  ela(licitate  babetur  reflexio  ;  ei^o«    P«  A« 

ItefleSitur  e,  c,  iumen  ab  aqua,  qux  tamen/  quin  com* 

yreiniis  non  eft,  elaftica  non  eft  ;  crgo,       ^,'  N«  A, 

Ad  Prpbt  {fumen  refleOi  tb  aqua  admitto  -,  nego  ta- 

snen  aquam  miniroe  elafticam  e(rei     4^t  cotnfrifm  ncm 

fuiu    Dicam  :  nequit  comprimi  (enfibiliterT.  A«  em« 

nino  eQmprimi  nequit  N»  A»  &  Cm,        Vapores  aqu^ 

lunty  flc  comprimi  po^funt  (enfibiliter;   hinc  dixi  T^ 

Czterum  e3(  elafticitate  non  comprefliiitas  inferri  de* 

l>et,  (ed  confttm  %wam  fmif  rmmmiiSm  V9c^ 

ttranidL 


nu 


l$n  virium.  f  59 

Illt  Qiiif  cr^^r  incad^m  ^  pilt  cadeMs,  tut  muf* 
inor  darifli^Q0i  a  (iibtiliffinia  locis  tnolecaU  compri- 
mi  ?  (iqne  non  comprifonntur :  motus  reflexi  caa£i  f2«« 
ftickaseflc  non  potcft ;  ergo.  tj/L*  Crcdunt  ii  omnes, 
^uibusyorpora  fe^eSe  dura  in  rerom  natara  nulla 
^nt.  De  luce  quod  additur ,  (ic  expono :  iucis  cemii* 
fatem  abande  compenfat  fidem  prope  omnem  exfupt^ 
,  isans  veiocitas  ( tres  enim  fupra  triginta  miliiones  levu 
carum  decisrrit  tntra  ^,  &  1}^^) ;  qoarenontemneii. 
4a  quantitu  motus  exiurgerc  debet* 

IV.  In  corpore  eodem  eadem  kabetar  vis  elafti- 
Ca;  proinde  fi  ifta  reflexionis  catt(a  fit,  omnia  impim 
gentia  eodem  modo  refledi  oportebit ;  n^n  aatem  fie 
refle£lantar  ;  ergo.  i^.  D.  A«  l^adem  habetur  vit 
claiUca  f »  08u  prhno  C.  A.  fiem^de  N.  A.  &  Cm*  Via 
claftica  in  a6lt;  (ecando  pendet  a  qaantitare  motos  cor- 
jporis  impingentiSy  five  a  vt  comprimente,  cui  (  per 
/iiefifk )  squatur*     Eft  rero  diverfi  ftpe  in  impin. 

!eni:ibas  vis  comprimens  ;   igttar  &  diverfi  i^  percall 
9  ^laflicitas  ;  proinde  &  dive^(a  reflcxio.         ' 

• 

Vj  Elafticitas  e^rporis  tmpmgentif  non  eft  eaafii 
reflexionis  ;  nec  igitur  corporis  percufft.  ]]|.  N.  Q. 
Corpus  nullum  potens  eft  fe  ipfum  determinare  ed 
snotum ;  determinaree  autem,  fi  elafticitas  Jmpiugentk 
csufii  eflfet  motus  rcflexi^  11.  Elafticitas  impingcntis 
^gir^eaione  oppofita  reflexioni ;  aequie  proinde  cau- 
A  efTe  reflexionis.  Nihii  horum  obtinet  \  fi  elafticitat 
tercufji  ftatiiatur  cimfii  motoa  r^flexi ;  ^rgo. 

VI.  Nonduntaxat  pcrctfflnm,  fed  & {mpingeni 
corpos  nititor  figoram  ^miflam  recaperar^ ;  crgo  fi  pcr- 
coffi,  fimiliter  impingcntiselalticitas  caufii  reflexioois  dici 
debet.  k.  D.  A,  nititar  atromqoe  figuram  recoperar^ 
impingcfis  tamen  nifii  hoc  fiio  tendit  dire€Mone  refl^ 
wam  ^pofiit  a  A,  Badem  dir^^ne,  im  t^tiik 


t54  ^^^  '«  CfiputW. 

pcrfigitur  N.  A.  D.  Cs.  crgo  iimiliter  impfngeii^b  elt- 
fiicitas  caa&  crit  rcflcxioiiis  in  carfore  percuffo^  li  ino« 
(ile  fic  C.  Cm.  Suzmct  propriz  N*  Cm,  ^ 

Vll.  EUfticitate  comprc(fi  cQfporis  dctcrminatiir 
jmpingcns  ad  quictem  ;  non  crgo  ad  motum  rcflcxum* 
Pr.  A.  Eiafticitas  sk  lis  cft ,  &  contraria  vi  compri« 
sncnti,  quare  altcra  aitera^i  clidcre  debct ;  cli(a  auteiii 
clafiicitatc  non  detcrminatup  corpur  impingcns  ad  ma* 
tum,  fcd  ad  (^ui^tcm  ;  ergo,  l^.  N.  A.  Ad  Prob. 
fljo :  yis  quidem  claftica  ^  lis,  &  cohtraria  cfl  vi  com- 
primcnti ,  non  tamcn  altcra  altcraii^  clidit  proptcrca  , 
4]tiod  non  fimul  habcai^tur  ambs.  Primum  itaqpc  vit 
liabetur  comprimcns  in  impingente;  huic  demum  pet 
reriflcntiam  percudi  oorporis  cliCx  fucccdit  vis  elalticft 
obftacuii,  quod  figuram  amiiTam  rccupcrat  fimul^  fimiil 
impingens  determinat  ad  rcficxionem, 

VUF.  Nirus  reTumendi  figuram  priorcm  (blum« 
tnodo  arguit  remotionem  impin^cntis  ad  intcrvaUunl 
no^i  amplius,  quam  cxigat  rdtitutio  partium  compre(vi 
farum  in  fitum  priorem  ;  efgo.  i^.  D.  A.  Corpus  ta^ 
wcn  reoiQtum  (eiegel.  §.  2.  recitata  )  in  motu  perfe* 
«fcrat  C,  A.*  filUtar  motu^remoti  jjam  oorports  H.A* 
<kCm» 

IX,  Juxta  legem  11.  Neutont :  tffe^um  uafurfi» 
WoliMtn  ejusdem  geueris  eadem  fnm  caiifa\-{cA  motus. 
4ire£lus,  &  reflexus  e>asdem  eorporis,  eadem  otrinqut 
Velocitatc  dciati ,  {lint  cffeSus  naturalcs  cjusdcm  gehe* 
fis  (  utrinque  enlm  bnbetur  cadem  qnantitas  motus)  ^ 
ergo  ^mborun^  eadcm  cft  cauft,  Motus  autcm  dirc£(i 
caufa  eiafiicitas  non  eft;  nec  igitmr  Toifiext.  ^.  D.  M» 
l^ffeduum  natarAlinoi  eiusdem  gencris  edcdem  ft\nt 
caufae  imtnediata  0.  M«  mediats^zz  determinanies  N.  M« 
P,,m.  motus  direa%  &  refiexus  (imc  effefius  e)asd^sn 


lex  vMumi  tjf 

m  MT.  tD^&Ctn.  Motus  dire&us  A  tUfttck^te  n<m 
^eterfninatar ,  CtA  «  corpojr^  quovis  irnpelt^tn^  c.  c«  t 
inanu'  lapid^m  projiciente ;  ttgo  ab  elafticitate  repeti 
non  debet.  At  ni(i  eiafticitas  dicatar  cau(a  d<^ermi<« 
fians  ad  refie^qnc0j  aiia  quidem  caufi  praefto  non  ^rit; 
proinde^ 

X«  Mptus  omnispendet  a  ¥i  morrice^  igitur  &  r^'' 
ilexus.  ^.  P«ndet «  vi  motrice  tanquaip  cau&  immc» 
diata  C*  A.  nsediata^  ac  determmante  N.  A,  6(  Cm. 

fipikramur^  imprejjioni  cuivis  extetnafdkcilc  ceduntp 
facilequc  itidcm  moW  inU^inoi  ^  ac  comfarmivos 
adhtittunh 

Sciol.  Ptacuit  Pbilofbpborum  nonnuUis  tria  flui^ 
d^rum  geuera  ^dnotare.  {mum  genas  ajunt  efTe  eo» 
rum,  in  quorum  partibus  majufcuiis  iiuUa  fenj^ilis  a^ 
traSio  ob&rvatur  ^  au^  repuljio,  In  exemplum  ponunC 
fiiiliumyfulwres^  &  alia  id  g^QS  aggrogata,  ,qasB  gra« 
liulis  pro^e  Isvigatis  conii:ent«  Ad  lldum  refarunt  ei 
foium  fluida^.quorum  moleculis  majoribus  ineft  nqtaii* 
lis  repnljioy  ut  airi^  vaporikus  a§ueif,&Cn  Qenus  Ilitium 
complefUtur  ea  ftuida  ^  quorum  moleculis  maj[oribu$ 
fenjibilis  inefl  attraQib^  quaiem  in  Mercuriq^  a^ua^Q, 

obfiaere  ceri^imos^ 

§.  76«  NAtura  fluidorum  (  eorum  prascU 
pue »  qua^  in  tertio  genere  locantur  )  reponsn^ 
4a  cfi  in  particulis  fera^  Jpk^fricis  ,  h«  e,  talibus  , 
^uarum  funS^  di/hribuia  Ji^t  in  mtras  fapirficiig 
€onccntricas  ^  ita^  ut  in  aqualihus  a  cmtrct  Mjianh 
tiis  scquaUter ,  nunfcroqua  pari  Jint  diffufk.    Prob. 

$i<;  in(ell^«  flui^ojum  pat^^  iiuUo  propi« 

.      ftcgo* 


titgw^  ntplicAntur  pharnomenji  a  fliiiditJM 

f^rofeoa*       Nam  I.    Eluidorum  pdrus  commove^ 
utttur  fatiU  »  a^  ah  inviam  feparabuntur  vi  ^uan^ 
tumcunquetxigua;    vi  enim  huic  utCunque  exi«' 
gux    exiguum    opponetur  impedimentum  ^ 
quia  non  nifi  coha^rentia  aliauarum  partiuni 

fiedetentim  ^  ac  rucce/Sve  luperari  debeat» 
I.  facHe  molecuUe  alue  circa  aliat  revolvcntur^  quin 
enot^s  cum  Partibus  \rcmotioribus  communicnurm 
Pendet  hoc  bhxnomenon  a  fuperficie  fphasri- 
ca  ^  &  (atis  Uvigata.  IJ[I,  Si  4fua  fiuidi/rum 
farticuU  ab  aliis  paula  magis  recejferint ,  continuB 
in  earundem  lecum  fuccedent  alis^  ficque  vires 
nttrahentes  t  ac  repellentes  mutuo  fe  (t  com» 
pen(abunt  t  &  asquilibritas  fluido  reftituetur. 
Qux  fuperant  phamomena  ^  dabit  Scholium 
pbhinc  lecundum* 

Schoh  7.  Cttm  (phcricas  Aaidorum  molcciiIfl«  no» 
inino,  inteiligo  moieculds  ionge  fabtiiifllmfls,  qafllet 
ocuium  Microfcopiis  quibuscunque  flrmatum  (tibterfai> 
gtfliic,  inquf  angufliflimfl  eorporum  intervflllfl  ie  infi- 

rmnu 

SchohJL  Sunt,  quc  dubium  tyrombai  raoveant ; 
f ximflm  dubitfltionem.  Quaruut  I,  Cur  difficultoi  ium^ 
gens  iividendi  a  fi  invicem  particuloi  folidas ;  uon  item 
fiuidas  f  Vf*  Quifl  in  fluidis  motus  particularum  circm 
farticulnt  liher  oh  tarum  uniformitatem  permitm ,  tte 
fiparemur  aiia  pofi  aliat ,  dum  in  fiiidis  vSr  in  latm 
,  «  «  .  ,  ^  aujguli  promineuttf ,  ac  figurarum  irregala^ 
ripflt  iff^diuue  yusmodi  liberum  tnotum  (  qui  fke  fiaa 
pmetionc  diftantiarum^)  £^  cogjUHt  divulfionem  pbtri» 
m^rum  particutarum  fimtd\    verbfl   (unt  Boskovichii. 

S^n  ipx^mplo  iUnMrflt  petito  a  fiifcicalo  virgflrun,  qui 


fi  toms  frMigt  debeac  fimul ,  didiciiltdt  fcnriccnr ;  at 
uttf  virgai  aI](B  firanguutur  poft  alias,  facill^  vindtor  re» 
fi&ntia. 

Sluamni  lU  CW,  /  TfflJMf  JiutJkiJarWM  imfi 
/id^t,  fniumqui  cobannfss^  adB^tmreA  c^nwo$ri  focu 
l^t  iu^us  Jkpi  difficultm  Hi  ^f/taudif  ab  iuvictm  far» 
tiaJif  ?  Cercf;  lapis  obli^ue  in  aquam  jadaa ,  aut  gUu 
biit  e  rormeoto  excuflTus  ex  aqua  refilit.     Cerce  fna« 

ram  refifiehciam  i^  aqua  firiildenda  experiuntar ,  qui 
(c  €X  editiore  loco  in  eam  prsciplces  aguni.  i|u 
triboendum  iftud  eft  ceieritm  ingemi  »  qoa  ii»  flul-» 
dum  aliquod  incnrricur  ;  tum  enim  nequeunt  ftr  trtm^ 
vitatetn  timporit  parciculs  ^lis  aliis  locura  cedcre ,  dc 
in  gyrtuiira^;  •hmff  eo  C4(a  fluida  re&ftunt  tum  minut^ 
fBftOi  iblida* 

feiu^ III,  Curfiuidomm  fmmtla  ( #. c«  4f[M ), 
fuee  cmfiriffioul  mulmm  refifimit^  divifiQnem  maff^^  a^ 
fiparati^nifi  partit  unius  ab  dtera  nou  impediani  f 
Ijlonquid  Iqlidorttm  partes  hoe  ffgrius  ieparantur,  qu0 
magis  com^reflloni »  aut  rarefadioni  rcfiftunt  ?  j|U 
DifficiUor  compreffio  ^  aut  rarefi^io  or|um  duxic  ea^ 
cp»  quod  maflfulaB  aqt^  in  confiniis  arcus  validiflim* 
repailemie  hsrentea  oomprlmi  debercnc  i>mmt  Jwtalp 
adeoque  a£Hone  eadem  (uperanda  fbrcc  inercia ,  a4  re* 
polfio  omnium  fimul  parcicularun)«  In  divifione'  por« 
tkMiis  aque«  uniu»  ab  alia^  iftud  noti  ebtinf t^  quia  dun* 
ta^t  (iiperanda  eft  refiftencia^  ac  cohiefio  no^  fiici»  Va» 
ttda  fonitularum  uau  Cf^um^  fid  ^aaru§uiam% 

^m  111«  SS  fiutdtrum  omntum  natttfd  repMtndA 
fit  in  maffitlie  fir$pemodum'  Jpiaridt ,  &*  cduceutricit  ^ 
^f^aerum  ptmSa  in  eequalihus  a  ctutro  diftamiit  ^qualiter 
Jmt  diftriimat  uudi  msyor^  aut  minar  corpornm  quo» 
tmndam  fluiditat  ? .    Jj^   repetenda  eft  ab  ingrcflfu  patr» 

llydarw  j|«inui4aA  hvccr^ncivi^^  vel  carundeai 

egccC 


tjg  SeBol  btptiiliV, 

egrcflfu ,  pfoinacque  a  turbato  virium  «quilibrio  intcc 
f  artcs  flai<ioriiai>  -  Scilicct*  ca  fiuidiriitcm  imminuunt, 
qu«  ftqiiabilem  punaoruin  diftributioncm,  vircsquc  in* 
i^c  ortas^^a^/vinum  dM^oncm  tollunt*  Iftud  vcro 
five  pct  higrcdbm  ^^^Barum  hctcrogcncarum  fierf 
poiTc,  five  per  egrcd^^Hno  non  vidct ;  ergo.  At*^ 
t^wfi^de  ingreffu  pafticuffimi  hcterogcneaf um  rcs  tnanw 
fcft«  fit  in  vino ,  qupd  Oepc  ftjuiditatc  diminuta  viftofi- 
tatem  indxjit»  Qiu  in  egrcffn  molccularum  hcicrogc* 
Hearum  labBfant,  iftis  in  excmplum  {intmctalla,  qufi 
quamdiu  bcne  muitas  ignis  particulas  omnia  dilccrpcn» 
tcs,  ac  d^iflbcianres  In  ft  continent,  fluida  |^nt ;  fublt-* 
tis  m^fRiIis  isiicjs  firma  cvadunn 

RogantV-    Cut  flttiiwnm  fndlecula  fimper  ttqul^ 
Ubrium  apfetam  }      l^.  quia  gravitatc  ,  vel  potius  pon«* 
idcfe  (ao  eonfque  ad  alias  infra  (e  pofitas  accedunt,  do* 
«ec  vUtepcflens,  &  Conta£lnm  immediaruiti  prdhlbcn» 
«atn  griivitatis  vim  penitns  elixiat ;  qnarc  ad  ^quilibf  i*  , 
tifttcm  pcfvcnirc ,  ax:  propc  ejusmodi  iimitcs  confifter^' 
debent ,  nltfa  q^uos  nuila  amplius  vis  attracliva  ad  £en» 
fijm  operetur.     Hinc  evenire  vidcmus,  iitgraviiatc  ae 
prcfiione  iti  qtiavis  fluidi  piirtc  diininma  partes  gravio* 
res  illuc  afRuant,  leviorcsque  de^  loco  (bo  cxtrudanc  > 
fiuidumqQt  affurgat  etmlque »  dmn  ^qmUbritini  rc^» 
ttiatuxv 

JiogitttVl,  Vuryiuidorum iomgtneaium  imkculd 
ifMnef  ud  libeU(m  fi  compofiant ,  h,  e.  JkperficiQm  hori^ 
zouti  p0rallehm  %itduam  ?  !^.  t]ina,  ^m  graVes  (mc^ 
lingulir,  fingulae  ob  cxiliratem  ^  rotunditatem ,  ac  ixv>>. 
ntcm  fiiatn*  flhe  irtipcdimcftto  toeuifn  graVitati  &«  de» 
bittnn  "occupabtrtit,  five  non  pfius  quicfctnt,'  quam  fiil*, 
g\il*  yquaHtcr  irtftincantlir ;  fic  Vcro  ruftineri  ncque»-' 
trnt ,  nifi  iibi  flvndum  ad  Hbellam  ft  fe  compofiierit  % 
ergot       Omfirm,   Si  pottid  qusdam  aqus  ultra  aliai 


Lfxvtrtm^  159. 

i^  que^  dfim  Dmni  ex  parce  sequabiUtcr  cotnprifliatur  ;  tt^' 

1  g(K     Quanquam  illa  floidi  bomog«nei  ad  libeUam  com* 

!  po(itio  locoin  iioii  habet  in    fuperficiebus  fluidoraoA 

^  oainiiio  vaftis,  quales  funt  inariunij  aut  lacuum  idmp* 

\  dum  ingencium;  iftorum  enim  &perficie«  ferc  convc* 

\  aia  eft>  quia  talcm.  adio  gravicacis  exigtt. 

;  Ditms*  VIU      Majorts  fluidorum   partel    fgn^ . 

l  T4m  fibaricam  non  hiduuHt ,  fed  vafis ,  qu9  <oircentut  ^ 
figuram  ajfumunt ;  nuUisqne  vafis  conflri^^s  in  omHcoi 
quaquaverfus  partem  dilatantur%       Cur^^  moUcul/e  fluide* 

L  r»m  miHimaJpJbarie^efint^  V^,  Partes  ilaidorum  maA 
)ord  va(is  coar^ats  figuram  X}uamlibet  induere  dfbent 

f         caufli  mobilitatis  fna\  vafis  non  coercit£  ad^IvbfiUam.  (e 

^  componere  dcbcnt  ob  aqualem  gratifatiSy  (ive  terrae  ac« 

trabentis'  aElionem ,   modo  inipcrficies  fluidi  a4nio4uiti 

I  vafta  iie^fit.     Minim«  ex  adverfo  mdecul«  fi  (phsri« 

cx  non  Tunt)  nec  flaida  omnem  inpartern  facile  coitt-' 
iDoveri ,  nec  2il!A  fluidltatis  ph^nomcna  explicari  po«  ^ 
ternnt.  ^ 

j^junt  VIII.    'Cur  finiiitas  major  minorve  nen  tari^ 
tati  rejfofidei ^  acdenfitaei  ?       "B^^    quia  non  a  {iimma 
particularnm ,  fcd  ab  earundem  fphsricitate ,  li^virate  ^ 
boroogcneitate»  i&  {pquali  pU)n£h)ruin  circirm  Ccntra  di* 
!  ilributione  pendct  ^uiditas.         Inflanti  quidefl^  quod 

j  ^aria  fluidorum  tmpeditid  (irtipediutit  enim  fluida  mo- 

tum  )  proficijcitur  a  denfitate  variay  nofk  fluidi^at  ipfa  ? 
Ift*  quia  fluidorum  impeditio  oHtur  ab  inerda  >  qua 
proportionata  eft  mafTz  ;  fluiditat  aliundcf  Urgetti 
parr^  t  lu  fluido  denfiore  mafor  efl  tmtua  parucuiaru»0 
9  mtraSio  (  c^uia  major  numcrus  pun£^orum  elementa* 
rium,  quorum  finglila  Viribus  attra£livis  pollertt  )  ;. 
fnajori  attraSioni  rejpondet  Vninor  )nobitirm  ;  mobiiitati 
direde  refpondet  flUiditlU  ;  quare  penes  ccrpOra  4enftora 
ftmorem  effe  dportet  fluiditatem',  qnod^faUit^  T^*  D. 
A.  Uk  fliudo  dcofiort  m^M  cft  u^Ktek  j^ticularutQ 


—4 


1^0  SiHh  l  dfuilir, 

mnSAo^  tfM  tadien  xqdabiHcer  agit  in  omnein  ptr^ 
tem,  &  qaidem  eadem  vi  ad  centrom  tendente  C.  A^ 
n^ii  fic  agic  N.  A.  &  Cm*  In  floido  denfiore  major 
bibetitr  ntimerut  pitnftomm  elementartum  ;  qiianta* 
<^nqtie  antem  ca  fint ,  non  tamen  in  aliaa  parttciilat 
lagunt  fingula  viribu^  (eorfim  fiimptia ;  (ed  yelat  fi  \m 
centro  {phaerat  colleda  forcnt  omiiia  ,  vi  compofita 
igimt  cnm.retiquis  omnibus^  &  agont  «quabiiiter  vx 
^asvtl  I  vieinas  pracctpue  ^  particulas  ^  agont  denique 
aaione  in  fingulartim  centra  tendcnte.  Qnod  fiepe  ma* 
/ori  attradioni  minor  rcfpondeat  mobilitas  C  pbtim 
mpfm  >  provenire  cen(eo  a  fbia  iterum  inertia ,  noit 
a  niajore  pu|idonHli  drquabilitcr  omHes  in  partes  agen* 
Ikm  numefo* 

$.  77«  Pfyjkorum  nmtutti  ftutJHstis  mtum 
rim  in  motu  ^uoJam  intefiino  farticularum  repo^ 
Jutrunt.  Non  (atis  rede ;  nam  I.  fatis,  credo^ 
fluiditas  intelfigitur  pofica  molecularum  ixili* 
t4tc,Jpbarmtdte^  glabritic ,  ac  prmodica  cobafiont  i 
qaxQ,  jam  optis  accetfere  motum  hunc  inteftU 
mim  ?  IL  Ex  motu  illo  noti  intelligitur  flut« 
ditis ;  fic  /blida  pleraque  multum  licec  cale^ 
fii^a^  proindeque  motu  vehementi  agitata  nu 
hilominus  (blida  manent)  Buida  non  cvadunt* 
IIL  Dift^  molecularum  agitatione  toUeretur 
vtrium  stquilibritas ;  quare  n^c  fluida  (e  f# 
ad  libellam  componere^  nec  eorundem  parti*' 
culae  mrnimat  figoram  Tphcricam  ir>duere  po(l 
fent;  induunt  autems  feque  ad  tibeUamcom'' 
ponunt;  ergo.  IV.  Quis  credat  aquae  mole<> 
Culas  (phfltra  conftriAas  >  ac  in  experitnento 
Florentino  vaUdiffime .  comprefiras  adu  ma« 
v*ri  {  tt  fliiidicyeai  rutm  oafiainictuiir.  V»  Si ' 


Lcx  virium^  l6l. 

pulver<5S,  limus,  /ordesquc  aliap  fluido  vehe* 
vnjentiiis  agitato  admifccantur  ,  innarant;  fta- 
gnahce  fluido  rubndLint,  (icqueindicium  prac« 
bent  nuUum  incer  flutdi  ftagnantis  particulas 
motum  haberi. 

Sch$L  L  Ne  iillns  logeinachine  locns  dctur,  no» 
taik  juvcrit  ?  inreftino  hoc  piartiam  motu  Venire  motnm 
quempiam  fingtilarem  ad  rarionem  fiuiditaris  pertinenf' 
tcm.  Hunc  dum  rejicia,  non  cadcm  opera  morum  il- 
lam  omnibiis  materire  pun£tis  communem  exeludo  > 
<juem  in  corporibus  etiam  firmis  dari  docni  in  Meti* 
ffyjica. 

Sdfol  IL  Opponunt  fenttntitp  adverfie  Pfltrdnl  L 
Fluidicas  non  datur  (ine  certo  caLoris  gradu ;  ubi  calor, 
ibi  motus ;  crgp.  V^.  motus  ii\t  ex  ccrto  caloris 
gradu  ortus  firmis  etiam  corporihns  cominunis  eft ; 
quare  ad  naturam,  ac  efTentiam  fluiditatis  pertinerc  haud 
poteft.  '^.  li.  ubi  calor,  ibi  motus  ;  Cxpe  ramen  iVi* 
Jitffciens  ad  commovendas  minimas  iluidi  particulas  C. 
A.  (cmpcr  fufficiens  N.  A,  &  Cm«  Addir  MufcLen^ 
brcekius  :  cerrura  cal6ris  gradum  ad  iluidi  niiruram  mi* 
jiimc  neceflarium  eflc  ;  unde  enim^iftud  evincatur  ?  iti 
e  Mercurio  ,  oUis  deftiUatis  ,  Jpiritu  vini  athereo  ?  Dixi 
(iipra :  motum  a  calore  profeflum  &pe  infufBcientem 
cftcad  motum  partium  fluidi;  non  enim  igni  fcmper 
tantiP  infunt  vires^  utpartium  graviras,  affri£!us,  &  vit 
cohaefiva  fupcrcrur. 

If.  Sublaro  calorc  liquida  cvadunr  firma  ^  quod 
paret  in  metiiliis  igne  liquefadis  frigore  in  maft^as  fir* 
mascoaguIati$«  itifertint :  crgo  ad  fiuiditarem  rcqui^ 
•  ritur  ignisi  &  morus  partium.  Sed*  pacc  iftorum  rcd^ 
dam  ego  :  NonnuUa  corporp  agenrc  <;aIorc  evadunr  fir* 
ma  ;  ignc  in  firmos  larcrcs  abir  moli^  lurunb,  indur^ruc 
ovoruni  albumai,  cret»  &c.  quare  trd  fluiJitatcm  nihil 

.1-    •  *  ad. 


^  I 


•dmodnin  eonfert  ignis,  &  motus  partiuin.  Hine  WxU 
tiir,re(pon(io  II.  fubldto  igne  iBuida  eradum  firma  per 
M€cidinSy<imti  vires  firmitatem  genemhtes  rubdu6lo,cfl]& 
lore  (e  exerere  pofTunt  C.  A»  tanquam  ii  ignes  mole» 
.cal«  fld  fiuidi  coafticutionem  fint  nec^£Uric  N^  A. 
&  Cm.  , 

N. 

ItL  Ftuidam  flutdo  permi(cetar  facile ,  quod  (in« 
intellino  pnrtium  motu  fieri  nequit ;  ergoJ  l^.  No« 
quit  permixtio  liaberi  ab(que  inteAino  pftrtium  mota^ 
orto  in  ipta  permixtione  C>  A»  prius  Iiabito  N.  A«  fic 
Cm.  Si  motus  inteftinus  haberetor  tnte  permixtionem^ 
jnajori  celeritate^  ac  veiuti  fiibito  permi^ecrcntur  fluidaj; 
tion  autem  adeo  celeriter  permi(centur ;  nam  tefte  Mum 
Jibeniroduo  vinum  rnbrnm  Italicum  ^  &  grave ,  noa 
f)rius  eommilcctor  aquat  infufie ,  qvamclapfis  i8.  mea* 
fibust 

iV.  Liquida  evaporant  \  nSn  antem  <ine  motu  paiv 
fium ;  ergo»  ^.  Eodem  argumento  ab  cxhalationk 
bus  petito  conficitur  motus  partium  inXeflinus  in  (gli» 
dis  \  nihil  proinde  confert  ad  fluiditatis  efientiam  ia 
mottt  reponendam,  ^.11.  Evaporant  liquidanon  finc 
fnotUffed  infufficiente  ad  fiuiditjitem  C»  A/fufficicnteNik 
A'  &  Cm.  Motum  vaporibiis  evibrandis  necefliriuni 
sninime  ad  lluiditatem  fufficerc  ^  conjicere  licet  tx  eo^ 
quod  ob(ervantibus  PerratUm^  Kraftio^  aliisquc  ma«. 
|or  fit  glaciei  evaporatiOi  quam  aquse^  nec  tamen  glacict 
£nida  fit  inftar  aqujr« 

V.  Solida  fluidis  injeOd  e.  e.  {ah'a  aquis  tmmink 
ftb  iisdetn  foivuntur  manifetto  motus  indieio,  ]^« 
moitus  in  ipfa  {blutione  orti  indicio  C«  A.  prseexifteiVi 
tis  N.  A.  &  Cm.  Dabo^neceirarium  cde  motum  par- 
tium  TtA.  alifls  floidorom  qualitates  e.  c.,ad  vim  iblvendi 
anetalla,  falia,  &c< ;  at  qua.tandem  confecutione  elicie* 

tir»  cnodci»  ad  flwdi  cogftisu^oncm  icquiri  ? 


Ixx  virium»  1^3 

SchltlL  Ad  fluida  rcTOCO  htitnida ,  Hquida,  & 
yriCcoCsky  inrer  qa«  noniuiiKs  difiingiiere  placinr.  Flul^ 
davoc^my  qu4)nim  parres  cutti  paruni  cohsreanr ,  ra*' 
fiui  y  ac  iiTipulliont  cutvis  fiicHe  ceduiir ,  a.c  coininoveri 
aptiflim^t  (um;  hiiK  in  fluidis  reponunr  comuium  fa* 
rinZy  lapidum  minutc  contritorumy  arenuJarum  &e» 
hiqtdda  dicanr,  quorum  prcrerea  (iiperficies  va(ig 
conffaridac  ad  libellam  (e  componunr,  aur  4]ii2  Iiumi 
effttft  iariflime  dTffluunr ,  quod  evenir  i'n  Mercurio. 
Hnmida  nominanr,  quz  corporibns  aliis  fadle  adli^renrp 
nr  aqaa«  Miht  fluidum  plernmque  dicitnr  ilKid ,  quod- 
fimul  fit  humidum^  VifcQfa  apellanr,  qwrum  dimtno^ 
ta  efi  fluiditas*  Dtminurionis  hujus  rarionem  repo- 
nnnt  in  eo,  quod  particulfe  figura  non  (aris  glabra  coi|. 
ftriflx  finr.  sdo  quod  punfta  in  moleculis  viicofi  cor* 
poris  paribns  a  centro  diftantiis  pari  numero  non  diftri- 
buanrtin  ^rio  qnod  magna  habearur  parricularnm  difl 
fimilinm)  ac  heterogenearum  conjunf^io,.  quam  olea,  re- 
iia?  (blurs  &c.  ia  chemica  fm.  4maly(i  egregie  manife» 
fiam  faciunt. 

§.  y%.FluldA  utcunque  rars  motum  f9fp$^ 
rnm  imftdiiint.  Cum  enim  corpora  nuila  pe^ 
netran  poflinc»  debet  corpus  in  motu  confti«< 
tutum  volumen  fluicfi  yolumini  fuo  :=:  ie  d^ 
loco  dimovere;  huic  vero  fui  dimotioni  rcfi- 
IHc  fluidum  per  vim  inertiae ,  ficqne  refiften- 
do  motum  impediti  quacenus  fcilicet  pars 
aliqua  virium  fuperandae  fluidorum  refiflen^ 
^  dx  impendltur» 

$.  7^  JS^imitur  ^antitds  impeJitionis  fiul^ 
Jlarum.  L  A  fluidi  Jenfitatt /^  majori  enim  den* 
fitati  mliior  refpondet  ^mafTa ;  'AnafTir  majorr 
major  iacrtia»    II.  Afiuidi  una^^tatf^  £7  vifcofi^t 


1^4  ScBiol  CaputlK 

tatci  oritur  fnim  vifcofitas  a  validioribas  co- 
hxfionis  limitibus ,  quam  reperiantur  in  flui- 
dis.  Fortior  illa  molecularum  coh^fio  mo» 
,tum  impedit.  IIL  A  corporu  incurrentis  fupcT'^ 
fcici  quatquo  fucric  amplior ,  hoc ma|or  flui- 
di  refiftentis  copia  removenda.  VJ.  A  corpo. 
fi$  incurrmtis  vchcitatc^  nam  cum  majori  ve)o- 
citate  fpatium  majus  decurratur  ,  plures  mo- 
lecula;  vaftius  illud  fpatium  occupantes  de  loco 
funt  depellendxy  pluribusque  moleculis  major 
velocicas  eodem  tempore  communicanda. 

Sthol,  QuemadniQduin  ^«^^/tf  j^iryi/if  motuni  im* 
pediant  y  .exa6le  referri  non  potefi^  cam  {ingulorain 
fluidorum  natura,  ac  vires  explorat^  nop  (inr.  .  Uni* 
ver(e  dicitur :  impeditionem  fluidorum  efle  in  rationf 
eompofita  dmfitatis^  Ql  quadrati  vclocitatis* 

Chemicac  proprietates. 

^.  80.  Fcrmc^ttatio  dicitur  tnotm  iUc  turhur 
Jcntuf  ,  qui  a  pcrmixtionc^  corporum  dijjimilium 
e.  c  aquae  fortis ,  &  limatur^  ferri  profici(ci 
foUt.  Motum  hunc  inteftfnum  plerunlquQ 
comitatur  fpuma ,  &  copiofa  aeris  elaftici  ex^ 
pulfio. 

SchohJ*  Chcmici  vehcmcntiores  motns  e^rve/ra/- 
tiam  dicere  (bknt,  Ijniorcs  nudzm /krmentationeni,  Efi  ' 
fcrvcfcentfe ,  aut  fcrm^ntatio  (  njam  rcvera  idcm  funt ) 
notatdr  in  quavis  permixtionc  iiuidorum  acidorxUm  aim 
alcaiinis,  h*  c.  flnidorum  nitrofbrum  cum  bituminoits  /  . 
aut  in  admixtionti  metallorcim  cum  /pir itn  liitti ,  \^ 
aquii  forti  &c«  Jt  ; 

.  •      ^   '      'M'S 


ttxvirium.  l6% 

Sehol.  IL  Si  mafTa  fermehtans  (it  bomogenea ,  il« 
lias  fermentatio  audit  fimplex  ebuUitio  \  fi  heterogeneM, 
Vocatar  futrefa^io.  Simplex  ebullitio  nuUam  'eflen« 
Ualem  in  corpora  inducit  mutationem  propterea  ,  quod 
fingulx  corporis  homogenei  moiecuix  =:  llbus  agant 
Viribus,  neque  prius  quiefcan^,  quam  mafla  ad  priorem 
partium  compofitionem  redierit*  Putrefa£tio  novam 
corpori  fermentanti  fpecicm  tribuit ;  nam  insquali  il- 
k-,  ac  diver(i(Iima  particularum  didiinilium  tSione  in 
aliam  longe  formam  moleculs  coale(cunt. 

^«  8 1  •  Caufa  fermcntationii  ifi^  in  turbato  par^ 
tium  fiuidi  squilikrio  per  admixtionem  Gorpo<' 
ti^  extranei  \  hoc  enim  admixto  exiguus  alt- 
quis  motas  tpinimis  fluidi  particulis  imprimi- 
tur  ,  &  aBquilibritas  toUiru-r  ,  qua  fublata  par- 
tes  mutuis  viribus  attradiva  ,  ac  repulfiva  al- 
ternis  fibi  fuccedencibus  in  fe  (e  agunt  ^.mo- 
tusgue  illos  vehementes,  ac  perturbatos  cienr» 

SeboL  L  Multum  conferf e  aerem  ad  fermcntatiO^ 
ties  docet  M u(chenbr(ek ;  CiMtm  fi  ex  fale  AlkaMuo  y  & 
ficido  omncm  aerem  bauferis ,  nuUa  fit  effervefceinia  ^  iiet 
fpuma^  quamvii  falia  fuerint  acfrrima.  Verba'  fiint  lau  • 
dati  Au£^oris*    . 

ScboL  Ili  Videbitur  fortc  condgnata  fermentatio- 
nis  caufa  minus  idonea  explanandij  tot ,  tantisque ,  ac 
tam  miris  effedibus ,  quaies  in  «fFcrveCrentiis  habcri 
quotidie  notamusl 

Oggeretur  primum  :  Si  fcobi  ferrcs  adjiciatur  lul- 

f)1iur  depuratum  ,  madaque  omnis  aqnis  diluta  ,  &  50» 
Ibras  appendens  humi  dcfo^iatur,  pott  9»  circiter  boraf 
fnmus  primnm,  deinceps  flamma  eru>ppet,  tcrraquc  fuc- 
cuti#car  metibiil  (ane  validifnmis;       «^p  jEri  tic^uato 

L  3  afto* 


l65  SiSiol  OpuUK       ,  ^^ 

•{Tnfa  frrgida  tuBnoros  cSeaM  non  mft  progenurr^ 
5U0  ff  oleo  caryoplaillorum  /piritus  nitri  concemra* 
tus  admifceatar^  inttio  dcnfas  fnmus  aflfttrgtt ,  (ubinde 
maflTa  efferrefcet^AaiRmftmque  concipiet*  Tam  ftupeiw 
^i  efFedus  ab  on^  partiuro  squilibritate  fablara,  a  per« 
laodka  LmpiUfione  oriantur  ?  Dicam  s-  oriuntixr  m 
jpcvmodicsL  ifnputiione  tanqaam  «  eaujk  txuduta^  &  oc» 
tafiotiali  C.  A.  imntediata  ^  Cf  effichute  N*  A.  &  Crn* 
Scio,  debere  effedum  omnem  cauftfa^  tmmediata^  ac 
totali  proportionatura  cfTe»  Eft  vero  in  cafii  ncxftro : 
Bam  momis  illerapidiffimut»  ac  cffedt  planc  ftupehd* 
immeJiate  f  rofictfcuntur  a  mntuis  particaUrom  fermen* 
tantiamVirtbns,  qxtx  paaUutam  immntau  molecnltraRi 
diftaotia  4n  iminenfum  excre(cere  poteft ;  tnediate  hm» 
i)eiitar  a  perexLigoa  illa  impreffione,  qua  partiom  «quii^ 
'  libritas  fubiata  fuit*  Atque  talt  cauCe  mediatar  efte£^tttt 
cx  {pquo  non  refpondere  docet  nofter  ille  Boskovicb  in 
lymbolo  (cquenre :  Emergat  (  ftribit  ille  )  >  mari  fati^ 
fdittts  mons^  per  cnjt^  tarera  difpcfita  fint  lierfw  /mi» 
dum  hkgeiites  lapidnm  prte^aHdhtm  moles  y  tnm ,  qtm 
viagis  afcenditur  ^  eo-  nul¥>re$  ,  idotiic  vetfvs  aprcem  lapiOi 
Jmty  y  infummo  monte  areuula  :  fitit  autemfert  tnmiia 
in  deqttilibrio>  pendentia  ita ,  Ht  m  reJpeSu^  moHf  exigu0 
Jevolvi  po§int*  .  Si  avicuia  iu  fumma  ntoutf  commovem 
areimlam  pede  ,  ea  decidit ,  i^  lapilhs  Jicum  de^icit,  qui^ 
dum  ruuut  ^  majores  lapides  fe^tm  tr^bunt ,  ^  bi>i<^ 
omum  iugentes  iUas  moles  ,  fit  ruina  tmmauis ,  S*  ingem 
,  viotm  ,  qui  decidentibus  ^  mare  omuibw  mare  ipfun$ 
€ommovet ,  ac  in  io  agiio/fionefn  ingentem ,  ^  ttftdat  im» 
ifHanes  eiet  y  motu  aquammi  veietnentiffimo  ditttiffime  per» 
durante.  AvictUa  4eqnilibrium  ar^nula  Jufiuht  vi  perm 
quam  exigua ,  reliquos  tftottts  gravitas  edidit ,  qua  oceom 
Ifipnem  agetidi  efl  naQia  ex  illo  ntotu  cxiguo  avicuU^ 
Jtiac  imago  qnadam  eft  virinm  inteflinarutu  ageutium^ 
§ihi  y  atm  vires  a-ejckrt  fojfln^  ist  imtnenjum  ^  mutata 
tncnnque  parrtmWflatiti^  innlto  adbuc  major  effkSlus  ba^ 
ieri  foierit  ^  qu/m  in  cafu  ffdwaiii  ^  qu0  quidem  per* 
•-*  'fevirai 


r  •  ^^* —  '""  r^^^^^^^^tmmmmmm 


L$x  vlrhim.  167 

pverat  taim^  mtSa  tantummodo  v^hcitM  d^fictifift  pit, 
09vm  acccltratm^s. 

OffonHHT  IL  Si  feffnbiitatiqnes  s  fublata  partiuiii 
•quillbritatc  proficifcantur,  cur  demum  evancfeunt,  nifi 
liova  (empcr  cau(a  i($  con&rvapdis  adhibeatur  ?  ^. 
^tifa  (bbindc  virhim  ^quilibi^itas  re(Vituitm:«  Ad  rc{& 
tttctoncm  illam  qonf^rt  1*  Aer  amhiei^ ,  <{ui  mot^m 
particuIa^Qni  fermentdnLttum  (cnfim  imminuit  ,^  f^bind^ 
€x(linguit*  II.  Heferogeuearttm  farticularutn  ,  quse  19 
fermentati,onQ  permifceiitur  femper  j^  ijicurjuf  {  tqm 
enim  a  cep^o  itinpre  defle^cnt  incurrentqs ,  (enfimquQ 
•d  €0S  d^veniient  iimites,  in  quibus  nova  virium' squiU« 
brrtis  obtineatur.  IIU  Maptla  avoUnte^^  qns  pnu9 
ofcillationem  egregie  auxerant  >  cum  cnim  harum  alix 
poft  alUs  dilt^jgfit  funt,  fw.  c^^mai^ent  cx^  qus  Intcr* 
|iis,  exterii^isqQe  a^ionibus  j/npedicl^aut  «locum  lA  foxw 
mcntationc  ^uavis  <^ot^i  foJiitvm^ 

(fppofi^  IJt  Si  fermentatioQts  csu&  mgdt^ta  (k 
liibiata  cqqiiibrita^ :  quomodo  iiou  qusevi^  ma^Ta  altcri 
•dmixta  ferment4.tion4;m  gQnerqit  ^  cuni  qu2vi«  mata 
<xigi\o  apta  Gt  atquiiibrium  toHerc?  J^  qnsvis  mo- 
|u  fuo'  idonea  cft  tollcre  sqi^itibrium  p^rtium  JifiJibU 
Jium  C.  A*  infenftbilium  N.  A.  In  qulbusdam  molecu* 
li$  in(cn(ibiUbv|s  fepc  nuUa  obiervatur  vis ,  quA  (c  fb 
mvitua  fivc  Jkppctant  ^  five  fugiani; ;  hi^J  $dmixtis  non 
tollefur  ^quijiibrit^s  illaruR[i  yirium  ,  qua.  ferraeimtioni 
de^ervhmt.  ^.  ado^  Non  quaevis  maffa  alteri  adoiixtt 
fcriTi.ent<it,  quia  no.n  quaf vis  ma^fa  acida  eft ,  vel  Alks»it 
|ia  C  A.  fi  alia  a<;ida  eft^j^lij^  ajkalii^a  N.  A^,  &  Cm, 
Sola  ctcida  cum  al}caUni$  fermenrtant.  Acida  cuoci »  aot 
{piQuli  figuram  iuduunt  c.  c  nitrum*  jilkajit^  poto^ 
lunt,  ac  ipoiigio(lc.  c.  cs^Ik^  met.aila  ,^  mineralia »  pcuij 
cancrorum  &c* ;  faciic  igitur  acida  .alkalinis  permi(cerf, 
inquc  i(ta  (e  infiuuarc  po/Tunt ;  ficji  ut  propius  a^ddaQ^ 

dJififfiyjimn  corp ocUjBi  particalae  «d  M  fttbuidc  diftaa* 

L  4      ^  titt 


r  -m. 


IjSi  ScSip  T.  Caput  IV. 

tias  deferantur  ,    in  quibas  mutuc  vices  &  fi  valeanc 
cxercrc. 

Dicetur  IV.  Si  tdntum  «cida  alkallnis  permixta 
fcrmcnrantj  ci:r  aqua  fortis  argcnto  afFufa  fcrmcntatio- 
Dem  crcat ,  non  item  afTuia  auTo  ?  Cur  cadcm  aqua 
£r)rtis  (alc  Aulmoniaco  imprsgnata  (  quo  ca(u  aqna  l^^- 
gif  farutarur  )  fcrmenrationem  ciet  in  moleculis  auri , 
lion  argenti  ?  Cur  fi  acetum  c(Jralliis,mcrcurio  fpiritus 
nitri  afFundatur,  habebitur  fermentatio  :  pon  fi  aliis  cor- 
poribus|  l^.  guia  non  omnia  corpora  rclate  ad  om* 
Siia  funt  acida,  vei  alkaiina,  fed  qu^^dam  comparatc  ad 
^liqua  func  acida,  con^paratc  ad  piia  Cunt  aikaltna^  quae 
idcirc9  falia  mcdia  ^  aut  fmitra  apellamtis.  Talia  £un| 
qusvis  dulcia,  >fu(phurca,  pinguia  &c. 

_  • 

Feteu  V,  Qnid  &pe  opus  aquam  affundcre  acidif, 
&  alkaiinis  miiruo  jam  admixtis  ?  (ic  nifi  iimarurx 
inartis,  ac  fulphuri  aqna  afFundarur  ,  fermcntatio  vix 
confurget.  '  :^.  Ut  aquis  affufis  moieculs  hcterogc- 
nca?  ad  cas  diltantias  devenire  poflint,  in  quibus  vire$ 
snutuas,  h.  c*  alis  alias  primum  appctci^i,  ambs  mosc 
ob  eiadicitarcm  refilife,  &  in  alias  incurrere,  ab  idis 
,  irerum  cum  impctu  cxcuti ,  itcrumque  in  partes  alias 
incurrerc,  pcrpetuoque  motu  perturbato  fcrri  pofllnt 

Teiet,  FI.  Fermcntantcs  mafiulfle  non  modo  rapi- 
difTimc  commoventur,  fed  dilTipantiir  ctiam ,  &  diffi- 
pantur  inaequalitcr*  Quacaufe?  Ij^,  quia  nonnulia 
'  particuicE  minimz  fliis  e  locis  -dimots  continuo  deve- 
niunt  ad  ampli(fimum  arcurh  repcilcntem ;  hinc  repel-  , 
luntur  validifl[ime.  Porro  :  quia  area  rcpcllens,  c  qua 
exploduntur  particulac,  jam  ampfior  cffe  potclt,  jam 
contraflior,  ab  arearum  divcrfitate  insqualitatem  difli- 
pationis  rcpctcndam  effe  puto» 


\ 


■r 


*  §.82. 


dx  vkinmm  I  ^9 

S'%2*  S$luiic  habecar  ^  cum  {blida  cer- 
4is  fluidis  (qaasiff<»/riiif  dicuntChemici)  ad* 
inixta  in  partes  minutiflimas  difcerpuntur^ 
quae  menftruis  fuis  velut  innatarit. 

Scbol.  L  Si  illa  (blidi  difcerptio ,  ac  moleculttnm 
minimaram.  feparatio  magna  celeritate,  ac  impejtu  pef* 
•gatur,  eorrofio  audit.  -  Si  partes  duntaxat  aliquflr  a  cor* 
pore  (eparantor »  reliquis  IntA^is ,  extra&io  nominattif« 
Ad  hane  pertinent  (ic  diStx  infiifiones  j  qualis  habetur^ 
ii  e.  c.  afFuiis  aquit,  cumprimis  calentibus,  e  Hgno  Brti» 
(ilb  extrahitur  (uccus  qnidam  ^  intra  iibras  latens  ,  U» 
gnum  non  di(cerpttur, 

Scboh  11.  Fluida  fokendis  corporibus'  idonet 
tnefiflrUa  dicimus  a  40  diehuS)  qui  iisdem  pleirunique  a 
Chemicis  tribuuntur»  Sunt  vero  diver(a .  diverfbrum 
corporum  menftrua,  Aqtta  (blvendis  (alibus  maxim6 
idonta  eft.  Eadem  immo  aqua  corpora  quarque  duriC 
iima.e.  c,  metalJa  difToIvit  lapdi  temporis«  Si  aquse 
^dmi(cc«ntur  (alia  qucdam  acida ,  vel  alkalina  (bluta, 
celerior  habetur  (biutio«  "  .//^«fl  fortis  (blvit  omnia 
snetalla,  aurum  (i  demas*  /Iqua  regis  aurum,  cuprum» 
/crrum  &c.  non  i^rgenttun.  Acetum  (blvit  plumbum  |. 
.cuprufn,  zmcum»  nonaurum,  argentum,  mercuriunv 
Idem  eft  de  aliis  menftruis,  ut  Jfiritu  uitri^  Jpiritufalif 
marini^  mercurio,  oleo  olivarum  ilfc» 

$•  83«  Caufs  fiJutiomi  efi,  quad  majfuU 
corporii  Jijfolvcndi  mofft  attrahantur  a  mokcuUi 
omnftrui  ^  ^uam  a  fi  invicm.  Hoc  enim  pafto 
£ert  debet  p  ut  aliie  poft  alias  aTcllantur  a  cor* 
pore  difcerpendo  ,  &  fingulae  a  particulis  > 
menftrai  ambiAntur ,  &  iis^m  veluti  fatu* 
remur»  ^ 

L  f         N.     ■       Scitt, 


176  SeSl$I.  CapfnlK 

SchK  Oixi  Citpra :  mafliilas  dinbcistas  Innatsr» 
tnefiflTQOt  Nom  vcro  non  mcrgi  dcberenc ,  ctiin  plo»  , 
rieque  graviratc  fpecifica  cxruperem  inenOrQum  quod»> 
Ifi&^  Kon,  iqquain  ;  vi&  cniin»  qus  madulas  corporis 
«iifcerpti  cum  molccalis  mcnllrui  confociac,  major  eft^ 
^am  vis  gravicatis^      , 

^.  ^4.    Solucianem    cxcipit  prdHpitMth^ 
qua  difrolutorum  cprporum  moieculac  fluido    . 
jnnatantes  ,  fubin^e  jilio  corpore   in  nien« 
firuum  immiiTo  ad  fondum  fubijdunt,  d 

Scbot  Notatlonefn  merctur  Whpr^cfphatiomm  conl 
Iceutiot  Unciae  argemi  ki  granda  redsQi  afFundc»' 
gcminas  aqtiafortis  ^  ^m /pirhm  nitri  uncias;  eflcrvo. 
fcct,  ac  diflbivctur  arg^entam*  Adjice  politam  Umcilani, 
VenerkS^^  ^^t^^  i  fiibfident  pqlvcres  argentci,  &  lamcl- 
la  falvetur,     Tum  impone  larocllam  Martu,  Ceu  f$rri  ^  j 

£^  praecipitafti  cuprum.  Fcrrum  adjie£la  ziftcp  ^  five 
fianuo  :,  iftud  ab  oculis  cancrortm  i  ilii  a  fpiritu  uriu^  i 
^jus  (^lia  ^b  alkali  ali^uo  fixo.  prcclpiuuc^r, 

^.  85^.    CmfA  prdcipiMiofiii  in  ۥ  eerfitur^ 

quod  c§rpui  jnm  perads  filtnimi  sdjedum  forHw 
trabat  fHdeculaf  menfirHi ,  ^Um  trahant  particuU 
€orpori$  ante  diffoluti.  Sic  enim  ma(ful2  corpo- 
ri$  primi  jam  di(cerpti  mcnftrqo  ambiente 
privabuntur^  &  urgente  fnajort  gravirate  fpc- 
cifica  ad  fundum  aelabentun  a 

SchoU  ht  cur  melccubc  prascrpftats  non  Atrm 
in  moicm  grandiorcm  coalcteunr  %  J^»  quia  ad  prir 
j^UQdi  cobjdlqnis  Ijauces  oon  f cftuieunt.  "-^ 

•    \    - . 


\ 


_ 


§.  960  t^ncrnio ,  aut  Gufguhiio  haberur , 
eam  &Hdufn  iiuid6  rmmiirunn ,  aut  diio  fluida 
(ibi  permtxta  abeunt  in  ma(Ias  firmas* 

ScAo/l  Sales'  in  aqua  (bluti»  ubi  hsc  cena  fiii  parto 
^aporaverir,  eoeiint  in  manuras  varia?  inagnitudinji » 
quas  tfyfiaUos  nominanms  i  hinc  (alium  feiucarufn  caoi 
,  cqua  concretio  pafllim  QryftdlHzatio  audit.  Caaguhnom 
•  fli;&  cxewpium  eft  in  alcohole  vini  cum  {piritu  urinx» 
vel  albumine  ovi  ^  vel  ifero  {angainis  permixtou  Ad 
concretionem  referri  polTunt  fnblimatiQHiS  »  ac  mifabi» 
les  illc  vegetationes  chnnica ,  qual^  cum  voluptatc  fye* 
Aamus  in  arlfore  Diatne  orta  ex  mixtione  argenti ,  fit 
mercurii ,  vel  arhore  Martk  c%  oiij&tionc  fcrri  ^  &  U« 
^uore  tartari  bata« 

§•  %7*  CcHcritioms  ,  toaguUlioms »  jr  ^r^M 
pallizationcs  rtHi  tribuuntur  vi  attroHiva^  qua  ur« 
/  gentefieri  patelt|  ut  moiecula?  duac>  fivetfi« 
terppiiru  aliarum  ,  fiye  aliarum  emigration« 
pcopius  ad  fe  fe  accedant»  quam  ante^  &  ad 
vaiidiores  coharfionum  iimites  deiatx  mafiam 
iirmam  efficiant,  ycgctaHoms  cbcmics  in^u^^ 
htdti  virium  tribucnJa  Jiint.  Cum  enim  in  m(h-* 
JecuHs  variis  varius  fic  pumftorum  numeruSi 
^cdifiributio,  varia  ^nafbitur  vtrium  compo- 
iitio.  Fit  igituti  ut  particula;  atiat  relate  ad 
itlras  vim  nullam  exeraht ,  aat  permodicam  : 
comparate  ad  alias  agant  viribos  8t  dire^io^ 
|ie  9  &  vigore  divirfiffimis, 

,  S*  88«  U^nMh  fit,  e^mfoMi  abeanttn 

iluida.     Abeunc  vero  (kpe  mingrtjftm  matm4 

Htji^^m  «»trtmt4t  i  Qc  irruptioao «  Qc  agicatio- 

Pf 


17*  SelHol   CapMlV. 

M  tgnis  ITquefciint  metalla,  vitra  &C.    Non* 
punquam    dfc  egrcjjmn  matcrU   hncrogenea\    fic^ 
plurima  corpora  vifcoG  ,   ac  tenacia  hoc  ma* 
gis  evadunr  fluida,  quo  magis  depurantur,  & 
moleculis  heceroge neis  eliberancur* 

SchoL  Qqa!  fotida  abierant  in  fiuida  aglcatlone  cor- 
Iporis  interponti ,  deficiente  .agitatione  rurfum  abeunt 
in  folida;  lic  tamen,  uc  liquidcm  corpus  liquatum  fu^ 
Tic  homogenehm^  ^,  c,  ceray  metaUa  &c. ,  priorcm  for- 
jnam'  rcuimat,  ac  firmitatem  ;  fi  heterogeneum^  e»  c.  la- 
pdef,  ligna  &c. ,  ncc  formam  priorera  refiimat ,  ncc 
firmitatem  \  ab  his'  enim  avelluntur  partes  o]eo&,qu2 
priert  ad'  firmam  cohjeiionem  faciebant ;  fiibinde  verd 
•dione  ignis  delats  funt  fub  arcum  repulfivum.  His 
fublatis  reliqus  non  amplius  £e  fe  attrahunc,  .(ckl  dilTb- 
«iat(E  inaii^nt  inftar  c^lci«,  aut  cinerum. 

§•  89«  LiquatMnii  iau/s  fcre  eft  vcbemcnt 
sgitMtio  muteria  folidum  ingredicntis  e.  e.  ignis ; 
qua  pofita  minimae  (blidi  moleculx  a  fe  mvi« 
ccm  disjundx  ctrca  axes  celerrime  convertun- 
tur,  ipque  omnempart^m  exerunt  vim  ad 
fenrutn  acqQalemi  qux  fluidorum  natura  eft* 

ScboL  Licec  diverft  habeantur  molccularum  dire^ 
Aiones ,  &  pun£ta  rjribus  diverfis  prsdica  ,  molecuke 
tamen  corporis  iiquati  agunt  undique  ad  {enfiim  cqua* 
iiter ,  qfuia  tanta  fibi  cclcricatc  {liccedunt,  ut  difcrimqi 
Virium  haud  obfervari  poffit. 


/         V 


'^     .  Scaio 


•«riw  .  '        \ 


])#  mstH  eorporum^  173 

V 

Seclio  II. 

De  Motu  Corporuin. 

^*  ^O.  JgmrAto  motu  mturam  ignorari  nem 
ajfc  eft,  lcnpCit  alicubi  Arijioteles ;  fic  rede  fcri- 
pm ,  omnis  enim  corporum  muratio ,  proin- 
deque  omnis  in  renim  naciira  efSsdus  motu 
peragitur.  Quare  tanta  eft  do<5trinx  praifen- 
tis  neceificas  ,  quanta  in  Phj/Jicis  eCh  poteft 
maxima. 

Caput  L 

Notiones,  ac  veritates  pracvia?. 

^.91.  Motus  eft  continua  ,  ac  fuccediva 
loci  mutatio.  Mobile ,  quod  locum  mutac« 
Mutatur  autem  locus  >  quoties  alio  ordine  (i- 
multaneis  coexifticur, 

ScboL  I.  Mucatio  loci  (ine  direQione,  ac  eekritate 
cohfiderari  nequit.  Hinc  afliduo  moncnt  Metaphyfici : 
in  ornhi  niobili  fj^eflahdam  cffe  dire8io7iem  ^  &  ahri* 
tarevu  Phyfici  ajunr  :  etiam  maffae  ratianem  habendaat 
cITe  ',  quantitatem  enim  moem  examinanc  ,  qnam  e^ 
majfa  in  ceUritatem  dtiQa  metiendam  ciTe  conAat  ex 
alias  di^lis. 

Dicitur  aiuem  direSio  linea  re^a^  juxta  quam  mo- 
bilc  d^to  momcnto  fiv^  progreditur  ^  five  frogrediniti" 
tur,  Infercs:  ctiam  corpus  in  lir^a  curva  incedeni 
direQiofie  aliqua  moveri ,  uititur  cn^m  linea  rcw^a  pro» 
grcdi^  <)uantainviscjas'dirc£tiQ  innngiilis  orbits  paQ» 
jlis  «lutctuTi  '^    '        Gtlu    * 


174  St^ft  CipuiJk 

Ctleritm  irocatur  «j^di^  moUUs  ,  qua  aftum  tfioA 
dmum  ffutium  dato  umpore  decurrminin^  Atii  vocant 
rmofmf»  umporis  sd  J^utium,  Utriqae  rcftc  ;  liquct 
cnim  lioc  ina|orcin  cflc  mobilis  'vciocitateni ,  quo  lon» 
gios  Q>atium  brcviori  temporc  dccurritur  :  contra  hoc 
minorcm ,  quo  brevius  (pacium  iongiori  tempore  con** 
jficitur.  Jam  claridirria  conlccutione  clicicst  quontttm^ 
ttfpMfii  fir  vmfm  div/fitxfrimi  ceUrisam  menfitram, 
S 

r 

Sdot.IL  Dtlfaribnirar  tektitai  !n  4i/oibf m,  &r«ft 
iafham*  Aifoiuta  efi)  qua  cor[Ais  (blatarie  itimpttim  , 
tc  fine  ulla  rclationc  ad  aiiud  corpu^  mocum ,  cenaoi 
dccfirrit  ^atitim.'  Selaeiva  cit,  pcr  qnam  corpor«dua 
ve!  «d  le  invicem  dKrcedunt^  vel  t  (e  (c  rcccdiint.  Sk 
mobiiis  j^  velocitas  ;S  C,  mobilis  aiterius  B  zS  e^ 
Acccdar  corpus  /4  aci  B  prtfcedcns,^  Ivnans  motum, 
•cccdct  corpus  u4  Coh  diifferenria  vetocitatum ;  quare 
aeleritas  relaeiva  hoc  cafu  s:  C  —  c«  Gemina  hsc 
Corpora  adverfis  dirc^^lionibus  motd  iibi  occurrant,  eric  - 
eorundcm  aleritas  relativa  ^  C+c,  Diftributio  hse 
llfiu  erit  cuinprimis  ad  matcfiain  de  eot^du  cerporum% 

5     ^ 
Schk  Ut  Si  C  s;  ~  ,  fiet  C  r  »  5.  id  eft^ 

iata  mehcha^ ,  ac  fenrpore  cogmftimr  jfatium^  JS  9eb^ 
ftieas  dueatrtr  ht  eempus^  Nemo  jam  mir^bitur  -Geome- 
tr«s ,  ijui  cum  quantitales  quasvis  lineis  exprimere  «• 
jnent,  it«  confiituum  t  ftper  reSam  t^primetitem  tim*  - 
fus  dttcatur  reSta  e^hihem  veiacitatem  ^  uref  '^nita  4f» 
fignat  ^atfujn  perturfTim,  Bene  habeiit  v  tireii  enlni. 
ctmfiitgere  debct^  fi  per  i*edam  referentem  tempue 
fioere  concipiator  ^e£la  exhibens  celcrit^tem  reli£lo  uti* 
dtque  fni  v>e(l;igio  ^  h.  c.  (i  .roc>a  ducatur  in  reftam  ( 
ergo  cum  CT  ts^  ^^  debct  isee  gcmte  dc%Jiarc  fpM 
tittei  dcciirraai»^  i.  Ifict  . 


I^  mttunrpmtmi  I7)_ 

PLetn,  T  !ti   *^*  b^e^  dat^Jpafi^,  ic  vtlocitam 

^    '  C 

.tcgfio/iinir  tempm ,  fi./fdtinfn  dhidaiur  ptr  velifcitaref9h' 

Sed  m  his  ^  aiiisqite  id  genus  exprefllotiibus  ,diligeilti(I 

.fimei   moffinte  taiUio^   adverttndum ,    iigno  s   non 

ttidicari  «qufllititem  quantitatum  abfolutarumy  (rd  dun« 

taxat  ratiomm ;   V.  g.  fi  ponatnr  x  sz  y  ^  id  fton  isk* 

d{cAt  quaittitatetft  x  aqmletiijejff!  akeri  jf  (  qmd  uen^a 

ieterogifM  fint  )  dum  5r  e.  g.  W/»  agefittm  denotat ,  y 

tempm  ;    Verfim  quod  x  jemfer  fit  nt  ^ ,  ita  Ua  fi  ta 

arefcat  iu  tripluf»  >  jf  quoque  fiaa  trifio  f/iajor^ 

S  t 

Sdioi.  IV.  Sl  C  as  -  ,  ittramqut  t  r-  — ;  erie 

t  t 

S      t 
h  Cl  t  vs  ^:  ^%     JBquaUa  tidm  ad sqoatia  ECr. 

T      t 
h*t.  eeieritates  Juarmrt  moiHiumfafit  futer/e^  ut  ra» 
siottas  Jpaeiorum  ad  eempof^  '. 

Erit  11»  C  i  0  iz  S  t:  t  T^  id  eft  ;  celerltatet 
/Sriff  ift  tatiofte  <omtifita  eX  dirt&a  fpatiortitn ,  i^  rtci» 
fraca  tifiiportim.     Ab  hac  veritace  pendcfnt  ^eUquc^ 

lli.  Si  i  sa    r>  fiet  C\:  c  ^   S:  s^ 
rV.  Si  5  £3   j.  crit  Ct  €  Si   tt  Tb 

V.  Si  C  -!  c  habebitur  Si  s  is:  Tt  f.  h.  t.fi 
teteritates  moHlium  fitfit  aqUales ,  fpatia  ptrturfa  fuise 
u$  tffftpara  ;  nara  pro  ma)ore,  vel  minotc  temporc  mo. 
bilia  ilit  cquali  veiocitatt  donara  majus,  vci  minus  C\7ai^ 
Ciam  dccurrent*  Anclyticft  dedu£}io  (ic  habet  c  Eft 
iper  mute  diBa)  C  i  e  :a  Stt  sT.  ergo  C  s  T  ^ 
cS t ;  /aSnm  euitn  medior^m  &c^  Dividcndo  utriii* 
que  picr  C  ai  c,  obtinebitur  t  T  :Si/S  t.  FA£(a  hse 
«rqQalia  fi>lvcQda  in  fropottionein  ctit  St  s  da    TNf» 

^»  £•  D*  ^  y 


_  I 


17^  StBoIT.  Csputh 

§.  92.  Motum  partimar  \n  fimpKcm^qni 
ab  unica  vi  procedit,  &  confofitum  ^  <\\xi  a  plu« 
ribus  virsbus  eodem  tecnpore,  (ed  dtredion6 
diYerfa  JA  idem  mobile  agentibus  proficifcU 
tur. 

ScboU  Oportct  tiinen  dirtSiones  ittarwn  virium 
non  ejfe  e  diatpetro  oppofim  ;  (ecus  aut  niobile  quiefcet^ 
fi  vircs  oppofita  aquales  funt  i  aut  fi  iuaqualet ,  fcretur 
duntaxat  fecunduin  direfiionem  vis  prsvalehtis.  Cer- 
te  motus  cowpofittis  nunquam  habebitur,  Oportet  If. 
noH  eandeni  y  aut  paraUelam  ejfe  virium  dirediouem } 
•  iilitcr  itcrum  inotus  Q)e£Vata  dire^ione  compofiiusnon 
confutget ,  fcd  duntaxat  mobile  feretur  vi  quidem  ac- 
qunli  fummac  virium  componcntinm  ,  dire£lione  ancem 
fingulis  viribus  communi.  Quare  debent  vireSi  fi^mO? 
re  Geometris  familiari  per  lineas  defigncnrur ,  flib  an* 
gulo  quopiam  confpirare  j  ficque  (c  habebunt  ut  laiera 
parallclogrammi.  c 

^»93«  Eft  motus  aliui  ^cquahilis  ^  quo 
^qualibus  temporibus  a^iquaiia  fpatia  de(;ur« 
runtur  ;  quare  mobile  motu  xquabili  progre- 
diens  movetur  celeritate  nec  au<9:a  ,  nec  im- 
rninuta.  Alius  accekratus  ^  vel  retardatus^  cum 
aequalibus  inftantibus  in^qualia  fpatia  confi-* 
ciuntur«  Uniformiter  acccUratus  ,  aut  retardatus 
babetur,  dum  a^qnatibus  temporibus  squalia 
refpondenc  celeritatum  incrementa,  vel  dc* 
trementa;  quare  in  hoc  motu  celeritates  cre« 
icerc  dicuntur  ut  tempora.    ^ 

CoroV.    Spi^ium  mom  aquahiti  decurfiin|  cxpri» 
mltur  per  reRanffitum  A  B^  D  (  fig.  yma)  •     Si  enini 

per 


pK  r^^Eion^  J!r  di^iianuio  teiopiis  ducifurrtQa  A  C 
irelQcicacim  c^ii^flHW^  refercns,  confurgec  reQangQlunf 
4tB  C\  .aiqoi  iftod  v^Utt  (patiiiin ,  curo  f  s  CT  i 
ftgo»  Coom  v^ro :  fpitiuni  fnotu.  mifortnit^  acukrt^ 
«9  de^uriom  «yp.ninicoc  f^r  maugnium  A  B  C  {  Figtf 
ft* ) »  ^91  fi  pe^  re£|am  A  B  deugoecur  cenipQS ,  ex» 
ptiaienc  tinoP  i  ^,  le,  3/"^  4^  celericatem  ex  hf^ 
pjocfacfi  tmffifynirer,  acfittrttam  ^  quse  &  in  inflantibui 
lingQlis  rai  v)BAi09J(n.relin<|uep:  concipiaiuur ,  obrinc^ 
bicur  area  Alariji  CKprimonf   (patiaai  ^   cam  deaufi 

-  %.  94»  MhtQ  nlias  divifiones  in  ntotam 
dif^Sum^  rejhx$m ,  &  rtfraSMm  f  item  in  mo- 
tam  fir^^um  ,  oUif ««  pftfjfSernm  »  pnuiuh^ 
fum^  in  inotum  ^er  m^cbin^  fimpUcet^  reSUi'- 
mum ,  arrviftv4ppf  8ec.  qtitbus  nomiotbus  ^uae^ 
nocionibGti  pronqm  t(t  inceUigerc,  Id  lani 
ago»  ttt»  quando  mottts  rodilifieu^  confijr* 
giLt0  801  cttrvilinens  ,  &  a  quibus  aterque 
tiribos  profidfeantur »  nianife(lum  fiat, 

mlUm  i^ikk  Hmmff.  Mqbit?  enim  a  vi  uni- 
csdeterminatttm  «/  «rrtam  JircSionem  in  ea* 
iImi  perieverat  vi  inf  rtiar,  cum  nulla  eiusdem 
mtttanddt  habeatur  ratio  fufficiens»  fi  non  ad^ 
fit  cattla  qujppiam  extrane^  mobile  determi- 
s  Mos  ad  motationem  direftionis ;  ergo, 

.      $.  96.    5i  m$biU  imPffUflV^  du^s  virdfitf^ 
futatmm  din&Wi  fnl  uiUur^  p^fr^Ugrsmmi^ 


grmmh  i 

m» 


SiUL 


•  1 


t^i  J^&hlT.  Ckpuit 

Scboh  fi.  C.  Si  globas  in  yt  exiftens  (l^.  f . )  ttti. 

|>eliatur  miiilu  a^teni  (ectmdum  direfiionem  AB,  eodem» 
tut  tempoT^  mana  altera  (etundum  diredionem^^C;  6e 
tamen.ut  quo  tempore  globos  pertingeret  tnotii  dequMbilt 
ck  A  in  B  ,  fiquidem  folt  diredione  AB  impeUcrew 
tur,  eodem  tdmpore  mota  pariter  lequflbili  deveniret 
cx  ^  in  C,  fi  Ibla  diredtone  j1  Cttcgeretur.  Dico  t 
globus  /i  vtribas  memoratis  fimul  tgentibns  ad  mo* 
tum  determinatus  deicribet  motu  compofito  DiagOQt^ 
lem  AD^.  ^  x 

^  Nam  dacatur  B  D  partllttlalad  d  C,  tterum«« 
quii  CD  paraHela  adl  ABy  qa«  compleanc  pa« 
nllelogrammam  AD.    Propter  yim  agemeitf 
direaione  AB,  perveniet  globus  ad  pun^otn 
dliquod  reaie  BD3  verfus  quam  dirediontt 
M  B  urgetur;  propterque  vimidireAione  A  G 
impellenteiti  deferetur  ad  punaum  quodpiam 
ttetx  C  B  i  verfus  banc  enim  itidetp  poficiw 
brgetur  ;    quare  neceQe  eft  perveniac  ad  li« 
fieam* B  D^  Sc  C  D.    «  Porro  nequtt  Garpas 
idem  (nifi  a  femetipfo  dividatur^  ac  bis  po» 
fiatur  )  «(Te  iri  duobiif  locii  diverfi)  ^   debet- 
ibrgo  pertingere  ad  punaum  lineis  B  D  ,Vfle^ 
S  B  cottimune  ;    quare  ex  A  deferetur  ih  JP» 
Deferetuf  autem  linea  feftaitufn  quod  corpiis 
fnotufti  perfeveret  in  fla<u  motus  unifbrmitec.:. 
in  diredufti  (  §.  2.  Cor.  I. ) ,  turn,  quod  argui» 
mentom  jnox  recicacum  fingulis  iinese  A  D  , 
punAis  applica«i  po(fit ;  quare  mobile'  fuccei^ 
five  in  fingulis  lineoe  hujus  puniftis  e(&,  h.  eu 
diagonaiem  paraUelogramm)  AB  CD  defcribe^ 
te  debebit     ^  Verita^  hac  lucakntiiss  per<pi># 
cmur.€LX  $t^requemei\ 


Dp  m$tu  corpwunh  179 

SM.  Z.  Dixi ;  frppter  vim  tgmim  4inSm§ . 
jiB,  Mceedet  ghbm  ai  pUH^m  atiqnoi  nSa  BD  \ 
118 m  quid  «ccelfutn  hunc  imp<diat?  m  diredio  ACl 
Sed  fasc  ficuc  non  adjuvat »  fic  ncque  impedit  accefliiiii 
illam  ,  cam  oppoHta  non  fit  linex  S  D ,  fed  paral}elji ; 
nihtlquc  proinde  oiTiciet  dircSio  //  C,  quo  mintit  elo* 
bus  sd  punttum  aliquod  linec  B  D  perveniax*  llcai 
obtinet  circa  accenutn  «d  lineaoi  CD. 

Sciol  n»  MenGira  motus  cofnpofitl  e(l  diagona*^ 
lif»  Camque  diagonalif  omnis  minor  fit  duol^0«  ip^ 
rallelogrimnii  iateribus  fimul  fiifnptis ,  patet  in  omnl 
snttuum  compofittanc^  aliquid  virium  abfikaarum  ^ 
]^iideque  &  ceUritatif  deperdi^  DeHruuntnr  nem* 
pe  vires ,  quc  mobile  dcHe£iere  poflent  4  diagooalL 
Qttie  vires  reliqus  funt  ^  fibl  addontur. 

Stiak  IIL  Inde  vero  fluit:  quo  obtufiof  fkmt 
cti|ulus ,  fbb  quo  vires  conQ>irant ,  hoc  piua  viriuna 
s^baarum  deperdi  ;  quo  acutior  eartmium  winm 
fiierit  angnfus^  hoc  deper^i  minus  ;  nam  p^tno  cafii 
smnor  ddcribitur  diagonalis  ,  altero  major« 

Schol  tV*  Non  modo  fi  du«  vires  componantnr  «  . 
fid  ^.fi  plures,  exfiirget  motus  conipoficus,  qnifaci* 
le  dercrmtnari  poteft  ha<f  metbodo  :  Urgeatur  mobila 
cedem  tempore  viribos  AB^  AC^  AD^  AE  {Vi^ 
iQiiia).  CompOttancur  pnmum  vircs  fM^oximie  AB^ 
^  AC^  complcto paraliclogrammo  ABC JFtlefcribetu» 
diagonalis  /9  E  lila  jungatur  tertic  A  D  ,  iterumqtie 
completo  parallelogi-ammo  AFGD  delcribetur  diago» 
nalis  A  G  i  qux  ex  prionbus  trinis  reidiltans  fi  qnTartft 
vi  ^  £  coTnponetur ,  obtmebictir  deiiique  di^^naKi  • 
A  H,  quae  ertt  vta  fnotus  ex  quatuor  illia  prioribos  n* 


4 


S^, 


t|o  SeSlioU.  Ctputf. 

Scbot.  K  Miroc  orilicatis  ^  atqne  ctiatn  amcenitatU 
cft  prsfens  di  virium,  ae  motuum  camfojhidnt  dofhrina. 
Ab  hac  pendet  cxplicatio  obviomin  quoromcanque 
p^snomenorum.  E*  C.  Navis  remomm  ope,  ac  fiumi'^ 
fiis  impem  a6U  viam  quandam  mediam  inif.  Pi(ces  iii 
«quis  progredi  volentes  utroqoe  latere  aquam  celerrime 
cauda  feriunt  1  doplicique  injpoKione  co|rpus  fiiam  dU 
ire£^ione  qnadam  media  promovent.  Aves  doplici  ala- 
irom  imf  ciu  ft  le  in  omnem  partem  fiiciUin»  il^fiunc 

SchoL  Vt.  Sed  non  minorem  in  tby/ick,  &  Afir^»      i 
nomicis  prxlertim  problematis  fotvendls »  ac  itmfl^atia* 
ne  effeQuum  per  partes^  utilitatem  babet  virium^  ac.mo* 
tuum  refolnuo  ^  qux  quidem  in  rerum  natuta  non  da« 
tur,  at  magno  ddftrin^  compendio  adhibetur  &pe<^ 
Fic  aut^  motunm  ^  ac  virium  refolmio ,  cum  vi3  uni*         . 
ca  iimplex  concipitur  ut  compofita  e  pluribus  ,  quibut 
conjuiidis  a^quivalet.     £t  quidni  motus,  aut  vis  fimplex 
confiderari  pofTint  ut  compofita ,  cum  Jpe^ata  direQio»         ' 
fi>,  ac  effe&U  idem  Gt^  (eu  motus  ab  unica  tantum  vi 
procedat  1  &u  a  pluribus  partralibus  unam  aliquam  to« 
tatem  componentibus  ?  cumqoe  |inea  qusvia  expriiTiens 
motum,  aut  mocai  proportionalem  vim,  efl*e  poillc  dia« 
gonalis  alicujus  parallelogrammi  ^ 

.  Scbol  VlL  Pofliuit  vero  circa  eandcm  diagonalem 
plurt  parallelogramma  defcribi  (  Fig»  ^ma  )  ;  quare 
patefl:  idem  motus  Jtmplex  fpedari  ut  procedcns  a  di^ 
vkrjis  viribus  compefitis  ,  eundem  tamen  motum  compe^  \ 

/Sum  producenribus*    Hinc  quia  omnes  iilse  vires  com^ 
l^^itif  eundcm  eiTefium  generant^  tudiunt  a^iip§llentit^ 

ff.  97.  Eiiam  »  /!  du^  vires  cpnfpirdnui  4^ 
gMt  a^uabiliter ^ui fi  Mib^e  vires  tadim  legraC'^ 
$$l$rint  motum^  M  ntmr^mt^  mMi  femper  r^* 

^  '        Sm    • 


.?. 


Msm  Jifr^  kmm^  Pono.  iirts  aitibas  (  qu4« 
rum  dire^ones  lineis  ABf  ic  AC  defignaba 
in  Fig.  lot.)  efle  uniformiter  mihrmus^  atqne 
ka  comparatas ,  ue  qao  tempoi^e  mobite  fola 
\i  iecundum  direAionem  A  B  agente  impuU 
fbm  decurreret  lineam  if  JSieodem  tempore  fola 
x\  A  Cadum  decurrat  lineam  A  C  Compleatur 
parallelogrammum  ASGD,  dividaaturque  dU 
red^iones  ambae  in  partes  e.  c  tresi  fic  tamep» 
ut  pro  ratione  virium  uhiformiur  accikrantium  no« 
va  urrinque »  &  «quaiia  finguHs  tempufcolis 
accedant  velocitatum  incrementa ;  li.  e«  ut  fit 
AFiAI::^  AE:AHi8irwCQmAl:AB 
0  AHt  AC  Dicoi  mobile  viribus  AF,  U 
if  fimpuirum.deveniet  in  Gi  viribus  AI^  Sc 
AHinK;  viribus^^,  &ifCinD  (§.96.). 
Sunt  vero  punAa  G,  K^  D  in  eadem  reftat 
quod  fic  ouendo  i  JF^  AI,  ScAB  (pcr  i&y- 
pothfim)  (unt  proporttonales  re<%is  F  (f^  tjt^ 
BD.aimAE^  FGi  AH  j^  IK;  AC^ 
BD.  Hsibtbunw  {^UAFGy  AIK^  ABD 
fimiiia  (  cun|  e^im  ci^ca  asquales  angulos  F, 
J^B  ktera  fint  proportionalia,  ^la  tuscTunt 
asquiangula»  proinde  &Iimilia).  Erit  trgm 
jFt  41:=^  AGi  AK\  iterumque  AI :  AB 
55  AKi  A  D.  Ergo  Ccut  AF,  A  I,  AB  i^^ 
cent  in  eadem  re^ ,  fimiliter  AGf  AK9  4D 
jacebunt  in  ^dem  reda.  Quid  igitur ,  nifi 
&  pun Aa  Gf  K^  D  ^,  \n  eadem  reifia  A  D. 
Per  ipfaautem  hae:c.  pon^a  mobile  decuri^ie 
lineam  iliam ;  ec||;p  moKile  vir^us  $juiJ$m  rff-^ 
uiris  palfain  defcribit  rlineam^r^^Eaei» 


%. 


.♦ 


^ 


x82  ABkilT.  C^i. 

miUm,  flc  rigidiuf  efteiidi  ^ oteft :  A^  -^SGy  AiK^ 
jtBD  finit  it^wig^U^  Oc  fifnilia  {quod  ibpft  mo* 
iKu};  quare  anguli  FAG^  lAK,  BADCmt  squa^ 
les*  Atqut  vero  nw  eirenr  x^ale» ,  fi  ^^  dam  punSbi 
Jv .(  S  jacent  in  eadem  ceSa  ,  erUm  ponda  G^  l^  O 
xonj^cerentineademreSas  ergo. 

S*^Z*  A  mo5i7i^  impiSitur  viriha  ^vtrfi^ 
ra^mi,e.  c.  quarum  una  (it  «quabititer  agefis^ 
attera  uniforfniter  accelerans ,  vet  retar- 
datis  9  aut  amb^  qutdem  acceierahtes  ^  fed 
nan  eadem  Iege>  defirihU  femper  Hneam  curvam. 
Pdho  rim  if  B  e(fe  «quabrlem  :  vim  4  C  uni-' 
farmiter  acctlcrMntm.  Fig«  1 3«  Itefum  diyidanttnr 
ambae  iii  tres  parces,  &  A  B  quidem  in  asqaales  , 
A  Cvero  in  inarqua)es,(edpro  ratione  unifrrmis 
accikraUcnis  fn^.  Mobiie  viribus  AF^fx,  AE 
,  impolfum  deferetur  in  <?,  viribus  AI ^  6c  AH 
IniC,  viribtts^jB,&i!CinD  (§.96.};  pnn- 
^"^vero  (7»  Kyl>  in  eadem  reAa  non  jacent ; 
nam  reAaer  AF^  At^  AB  ex  hypothcfi  non 
funt proportionales  fe<ais  AB^AH^AC^  qua- 
re  irec  proportronales  fuot  re<9ts  pG^IKfBD. 
Non  igitur  cjonfurgent  £^h  AFG^AlKf4BI> 
aequiangula,  &  fimiiia;  prQindeque  non  ha-» 
bebitur  proportio  i  ABx  AI  :=i  AG:  AK; 
ZQt  A  I :  A  B  :=:  AKx  At).  Cum  ergo  Ii« 
neas  A  F\  A  I^  A  B  jaceatat  in  eadem  reda , 
A  Gf  AK^  ^ £>  noa  facebunt  in  eadem  rci^a^ 
dtqoe  adeo  neque  p^Aa  6,  K^  2),  Sed  fi 
^  sftud  ;  niobiie  tiei^ibet  curVam ,  cum  lincfli 
curva  concipiatur  ex  infinite  parril  diagonji* 

4^  mm  «Qoipoiitti  v^9^  :^  - 


\ 


Wt  m9^  eorptrm:  it) 

SdM.  h  R-rfttm  nieneo  :  rigi4i«i  *5«  4«»o«gJ 
«i  G^^K ,  D  noto  jacere  in  eadem  rcat.  A»  /«*y^ 
!il  K  .  &  v<BI>  noa  funt  «quian^l-,  &  finutoi 


dem  refta ;  ergo. 

ScboLlL   NuUns  erit  Phyfieui ,  fi  «d  prefinMjn 

aoOrinam  nin  perpetuo admtet.     C«P« ^"'^S 

q«e  projeftam  in  motn  conftiHitum  «  ^t^  cjm^ 

^  JieriVium  fuum.  ae  «overi^«aba«erj«  jr«j«^ 

tionem  ftatus;  quart  viriiuf  i^trfi  ffmn  •*»  «••. 
"  ftribee  cwyam. 

•  Caput IL 

•        ■  »       *  ' 

Pe  viribus,  &  menfura  virium; 

I  _^  •     , 

f ,  99.  mrtt  aStiv*  mifai  funt  ♦  qa«  cor- 
poris  ftaturri  ab  ipft  inertia  requiCt«im  pew 
turbant.  Tales  funt  wiftnHrtbiUM  m  impul- 
lione  aliorum  corpomm,  grM^t  tl^itiw,  e— 
fn^  >  firmenMio  ife, 

^,  100»  OmolcgiVim  partiuntur  in  vivsmf 
&  tnermm,  Vts  viva  dicitur.  qux  cum  aauali 
motione  conjunaa  eft .  «  fi  platw  fobduao 
corpui  graVe  libere  defcendat.  Vumortu^tV, 
V>s  oblUcMlo  iropedittr ,  ac  proind»  w  lol», 
conatu  moYeftdi  ttta. 


.  / 


SeB&f.  Xftrmtqac  vis  firpe  memfibeitnfe  Tli7(!ei  « 
CQmptmiis  Cartefiotti ,  &  LeiMM^Mui^  quot  incer  life 
^.  C>rAr/£iiii  toti  (nnt  in  eo^  iir  cai|ioPim  vivam»  qHant 
Qcrtuam  ex  ma(ta  in  cciericarem  daAi  «ftimaitdaat 
idBb  denioiiltrem*  <^i  Leiiuitsiiutn  feflantury  vim  i^ 
wn  noQ  ceteriuee,  ie4  fuMdrma  uUrnatk  metittnmr* 

^.lOl/  Audoro  B&fc6vifbi9^  fic  etiam  mfir 
9^#/  n^iv^i  diftingifendum  :  i^  vii  aHivAfft' 
wi^gimfis^  qwB  unico  \A\i  vartuo,  unico  tem«» 
^pons  momento  genorat  vetocitarem  finitam^ 
rajusrtiodi  commanteer  effe  cenfetur  iiiipal]- 
l^isYeiate  ad  prim^  /upei^ficies^  qus  fe  con« 
tingunc.  Eil  icem  %ns  sBimpcundi  generis  » 
qaa&  momento  temports  folam  prelfionem 
exercet»  qii«  in  veFbdtiifem  ^ion  tranfeat^  nt« 
ii  continao  aliquo  tempi»ri&  intervalio »  quo 
jp(a  preflio  duret  fine  impedimento^  five  fifMi 
contrarta  ssli  preffione* 

Schl  I.  Vim  aQiram  primi  generit»  Cevk  xmpuMioi» 
fiem  C^u*  i^roprie  rtcm  daitir  ,  nani  efFe&iis  irnpulfia* 
His  re£tits  tribuun(u|r  rQ>iy$fei» )  mdtiri  lic^t  4  md^» 
^Ui  unico  illo  idu  fiitoui  {g[eneratiir«  Vlm  aSipam  fi» 
mmdi  generis  mctmw  a  n^oru  genito,  filt^olqtie  a  tenfii. 
pore,  qoo  motus  gencraiur ;  ita  ^iitiiium»  ut  divtrfii 
k^jusrmdi  vires  ngeuM  eadem  tempere^  generent  motui 
fibi  mutuo  proportionatea;  eademper^  vie  agepr  divftrm 
fic  tetf^erihus  gcneret  mottt$  temparibus  prQportionalee, 

Sct$l.  tl^  Duo'  acRnic  monite  ex  eodem  hlo  Befi§^ 
viMo  depronliam  r  ntterum  ad  eelerkatem  pertinct ,  «K 
terum^  ad  laimpm ;  ^  utttin^qftie  «d  diflfoli^d^  varia  01« 
iphiiinafi  condudt  megiiopere. 

^      *'  ./.-.'  I,Ve- 


/ 

/ 


1«  Vtlocimtt  namcii  (inqiiit  ilfe')-!!)  ptdMi 
nAirpaito  t  Mcchtnicii,  «qmvQCcivi  ^  \  poccft  cmm 
figtuficarc  v€hcit4Hm  aStuakm »  qQ9  lumirfini  cft  ffcli(* 
tiQ  qQ«dain  in  motu  s^  bili  ^atii  pcrcurfi  divifi  pcr  Hvn» 
ims ,  quo  perciirriKir.  £t  porcft  fignificcrc  quandam^, 
quam  apto  SchciaftiCQrum  voci^bulo  fouiitiakm  appcL 
lo».  quc  nimirom  ^ft  dctcrminatio  ad  adqaUm^  fivo  de* 
tcrminatio ,  qQam  babct  mobilc ,  Ji  nttUa  vis  mutatio« 
Kicm  inducat^  percarrcndi  motu  =:  bili  dctcrminatudi 
iqdoddafti  {patium  quovis  dctcrminato  temporc.  Prinft 
ftabcri  'tiQh  pdtcft  mbmcmo  temporis,  fed  rcqnirit  tcill*^ 
|kia  cbntifiu^m ,  quo  motus  fiat»  &  rcquirit  motuih 
rsbilcm  ad  accuratafn  (l^i  ^cntnram.  Altcriam  intet« 
igant  McdUnicii  eum  JUlm  dfonmticd  cffoi^niann 


II.  Tcmpitt  In  mom  ^gsi^  m  vltiim  ficuuiigtm 

HktHr  ttuplicitcr  {|»cfiari  )iareft<    ftab  ?  qaatcntlc  mortft 

ille  a  viribaa  acccptiir,  insajore ,  yA  Ikiintirc  tcmpa/^ 

^urat  i  co  enim  major  crit  motut»  quo  cstcris  Jiaribat 

4ttf«vcrit  4iiittua^    Hoc  icnip»f  pcf^tiadt  nad  aAaalcqi 

motum  »  ncc  in  arftimanda  vi  confidcfatar ,  in  qot  ^ 

tittf  confidcrari  iolct  motua  qviidam  potcntialia,  {qh 

^ctcrmihatio    omnium  particularum   ad  percurtendt 

dtto  <]uodam  tcmporc  quaedatti  (patia*     sdo  ;  quatc* 

'ima  via;  '&  adio  iip(a'^rpctao  motun^progigncna  diuH 

^tivs  dHrat,  co  cnim  cft  mayov  ii|c  porcntiaiis  motus»  9; 

'^k  it&mVi^  motvs  tcm|iQri  dcbitoSi  ipo  mcjQrc  (Ctti]^« 

fc  cgcrit  vis  afiiva^ 

§:  ^  1 02.  Adhuc  vtm  monAcm  aU  mitin^ 
lfjr#  leGernere  |uvar«  Pis  m^trixtR^  qu«  ad 
niotutn  genitum  refer^ur  t  &  refpQndet  eefaN 
ritati  genh^  du^as  in  maflani »  in  qua  ipla 

§|MeratuY«  Viracccln^Mrix^ci^a^  a  maflk  pr«.(cict- 
it|8e  (blum  refpicit  celerititeniain  qiiacunquo 

maifii  flt«   Hipc  ooyam  id«ojndem  «ddii  mo« 

M|         •  biU 


t96  SiSioIL  OtfmtfL 

f>ilt  inifK<ISoi|6in  ;  fiqiie  noTa  Hla  impolfio 
tempel*  tadeoi  «fl  ^  &  c«teris  ?3lis,  K  e.  fi 

SuaHbttS  temportbus   xqaalii    refpondeant 
eritatum  incrementa»  dicitur  vitactikr^^ 

Sebok   Vis  motrix  recitato  (enfu  expolTta  aliter 

f' mi«r  nomintri  roler.  Vis  accelcratrix  gravim  c(i. 
ondvs  in  divcrfis  corporibus  diycrfiim  e&,  pro>  gravi- 
fatc  (cilicet  mtStut  majoris,  vel  minoris*  Ggivittt  k$ 
diverfiS  corporiboa  (  Qtcunque  magna,  aut  parva  iint) 
cadem  eft,  cam  eandem  in  illis  ex  etdem  altitudine  de- 
labcntibui  velocitatcm  gcmeret  eodcm  tcinporc  Si 
globas  plumbcus,  &  argillaccus  ex  eadem  altitudihe  de« 
niictantur  jif  v^ciio.,  eadem  ad  (enfimi  velocitate  deci- 
,dunt ;  quare  gravim  eadem  ^  eft  in  urroquc,  A%  QOn 
vif  mtrix^  cmii  pl^mbum  denfioa  fit  argilia*   ^,- .. 

i  S*  lO|^  Viritfm  omnium  quantitatem » 
^e  energiain  metimnr  ab  ef&du ,  qni  caulis 
'itiis  proportionalis  (emper  efle  debet,  '  Soli^ 
cite  vero  circumrpiciendum,quis  efieAuscauf^ 
cuique  tribaatur :  motusne  \  an  celeritas  fola  i 
Sedulo  item  advertendum  »  num  canfii  unm 
ttniporii  mowwM  0gat^  an  ^ommuo  sUfuo  Um^ 

rit  imtrvMoM 

S^  I04«  Mmfura  virium  aSivMrum  ttm  gf^ 
mrit  efi  maffk  duEta  in  celmtotem ;  fevt  F  ^  MC^ 
Hoc  enim  majer  yrh  e&  adbibenda »  quo  mo- 
bilis  mafla  fiierit  major ,  aut  qao  major  velo^ 
^tas  Gorpori  copciliandji« 

\ . 


X 

J>i  miu  ^&rfmtm.  187 

&hL  Jn  ifien(ara  viritifii  non  fitm  vtkdtatm 
eonfiderandam  tffe  ^  fe<i  motum  inde  Uqaet,  qaod 
vis  fnobtlt  appticata  velocitatem  generar  m  •tmukm 
farticulif;  fumma  aatem  otmiwm  efft&uum  afiionem 
metitnr ;  adeoque^iK»9Mr  omnhm  vctocitatum  iu  omni' 
ius  particulif  genitaram  debet  metiri  ?im.  Obtinebi« , 
tur  vcro  bsc  fumma ,  it  velocitas ,  qaz  "fingalis  pafti> 
.colia  eadem  commumcatari  multiplicabimr  per  niallam« 

Sebol  IL  Leibnitziani  menloram  rirtam  vivanim 

lepetanr  a  ma(^  maltipUcata  per  qaadrttum  otlertta* 

tis;  adeoque  iftis  dicitar  J^=3  MCC.     Stcaatem  ar* 

guunt :  -omnis  vis  efFedai  fuo  proportionata  eft  ;  (ed 

•iFe£^us  virium  vivarum  ^ft  (emper  proportionatas  qoa  • 

4rato  velocitatum  \  proinde  &  vires  viv«  (tmt  propor- 

tionatse  qaadrato   velocitatom,      Minorem  probaturi 

provooint  ad  esCperientias  >  qa«  omnes  in  idem  reci- 

.  dunt.     Ponunt  geminas  glandes  plumbeas  ^  Qc  B  mo- 

)e,  figora,  &  quantitate  =:  les.     Delabatur  (  ajant)  glo^ 

bas  ^  per  unotn  minutam  (ecundum ;   giobas  B  per 

9  '>•    Primus  nonnift  .1 5  ped.  percurret,  alter  6as  qoa- 

re  (patiam  a  glande  ^percur(um  ell  ad  (patium  ab  altera 

» fonfedum  ut  1 5  :  ^o ;  h.  e.  ati  i  ?  4.    Inferant :  er« 

gp  etiam  earvim  vires  (unt  ut  1 1  4.     Sed  i  6c  4  (iiitt 

qaadrata  de  i  &  a  ;  ergo«     Sed  enim  ratiociiiationeda 

hanc  paraiogijmum  effe  lcxfbit  P.  Henric.  PauliaHf  quod 

Qt  planum  faciatj^  non  ab(tmilem  aUom  parfklq|i(inuni 

gddocit  t  Petrus,  &  Pauiua  iter  agunt  s  bua  impedi* 

>  tnentis  onufli.    Conficiat  Fetras  tevcam  anam  tertipore 

borae  anios,  Paulua  qoataor  teinpore  binaram  horarum» 

Evidena  tR,  quod  effedus,  quem  gcnerat  vis  primt,  non 

fit  nifi-^quarta  portio  e(i«dti9,  quem  gignit  vis  (ecnn^. 

*  Non  tamen  refie  inde  conjieitar :  vim  primi  non  aliad 

'«(Te,  quatn  quartam  partem  virium  (ecundi.    Cur  vero? 

•^a  fcilicet  Paalus ,  ut  vim  quadmpkm  Petri  obtinear^ 

fion  tempore  borarum  dwtrum  ^jJkA  ituktt  dtmtaxic 

|W«9r  ^vQu  cmctki  dcbmt^  /f^ikgitm  i^v^^  vi« 


j3om  io  M  tft^  qQod  ^:  cum  dc  rpacio  p«rciir&>«gitar  , 
DuU^i  caiDcn  btbWttc  ratio   tcQfiporifl  impeofi.     iflud 
tgnnc  Ldhutzf0ni  i  Globnt  £  60  pecL  ilecurric,cuin  iiu. 
teret  globus  W  folnm  decurrtt^i  S,     Sq4  vero  deUbicur 
globui  £  ib^obut  miuuHf ,  globus  A  onico.     Quare  vU 
res  amboruni  non  fm;i(  in  raiiQne  Q>aciorum  dc^cvirib* 
XVkxn  abfolute  ^e£laui:un\  (ed  in  ratiane  rpacioram  4i* 
viibrum  per  cempijic,     Eric  ergo  via  globi  A  ad  viat         1 
globi  B  ut  |s  I  =)   I :  tf*      Ipfii  imma  experiencia 
«vtncet :  vixu  vivunon  (^w,  rttionem  duplidKam  c^ 
Iericatum«        $it  elobi  \^  q?«if&  ].  tibrar«m  ,  irehiei-        j 
fas  CiS    I  ;  (ic  globi  J9t  mafia  =s    l  libr.   celeritas  39  ^ 

)•  $i  direfttombttf  concrariis  impulfi  ^bo  mut^o 
libi  occurrenc,  FCgredienHir  ^nisque  poft  impulfionetn 
fa^am,  ferenttiF^uK»  etdem  vdocitate  (quod  ^x  obierva* 
tionibus  cj^niUt) ,  qua  paullo  mox  adyenerantt^  apor« 
fet  ergo  globof  iiloi  sr^li  ance  conflicium  vi  predicoi  , 

SaiCk»  Non  autem  fuifisnc  ^  les  ance  eonfli^m  vireSi^ 
fi  vires  metien<|aB  tffmt  p  mafla  muUtpltetta  por  qua- 
dratara  c^lentacit  ^  vis  «nim  ^bi  •A  &i(lec  =4  ) » globi 

Si  lieibnirsjani  dc^ma  koc  {cmm  «x  eo  ckrivanr^ 
4|ttod  corpus  VHribiis  compoficis  impulfum  ^tiagonalem 
^ercurrat  intra  id«m  tempus^  incra  qiiad  kterafeorfim 
jpedata  ^ercnrrifier  virit^s  GmpUcibus  aclam»  errartt 
jnagnopereit  (fon  adveriunc  partem  virium  in  colU- 
fioni^  Aeund«iii  deierminajwn^m  angutarem  deftrui ; 
quare  nuciqutro.  viacDmpo%a|  qua  cdrpus  hyrpotbena-  , 

um  dcftribiti  iammse  viriam  fimpUcium  feorfim  fpc* 
^atacum  7:  Ui  ^ttk  potaft.  St  trero  1  qoamvis  quadra*  t 
tom  hiypo,Ai9m(k  ^le  fit  qaadratit  reUquorum  late* 
'rum  fimiii  fiimptia,  non  camen  bypocbenuia  xque  lon- 
^•eftj^  nt  ii^a-^r^tiqwa  lafera  fimul  fuoipta  adaquet, 
^fuare  nectvis^,;per  qnam  corput  de(cribit  bypochemi* 

)imt,  ^  U»  cft •? iribai  itmplfteibatiaorfim  fumj^tis; 

•  \     '  5.10$ 


i. 


§.  105.  Menfur*  virium  ^iv^orm  fcctm^ 
gmtris  Hi4m  tft  majf^  duHd  in  if^l^bshm  $  ftd 
ctim  vis*  ill^  3ga(  contihuo  aliqoo  tempi^re;^ 
erit  vis  mukiplicau  per  fompus  ttlfs  maffir 
du^  in  ccltBritatiiro  5  hie^.^Tsi:  4MC    Fa- 

MC 
Aa  utrinque  diyifione  ptt  r  erit  T  s:  ^ 


r 


&i(»l  in  iflit  mivdetii  vinbuc  idSmetiettdis  noti 
tnodo  rtf//d  effkBuam  btbcri  dcbec ,  fed  &  fmjnr^m  > 
^aibas  generantur*  Sic  duphs  habert  Vires  diciincis  ' 
cos,  (fd  dtipium  opul»  eodem  temporC)  vel  idem  odus 
brevtort  temtK>re  perficittnt.  SAtis  etiam  patet  tznitm 
tm  :si  iibtts  «emporibut  eosilem  pro^iitre  dTcatts. 

^  ^.  tCM^.  Bnerjjia  vii  acetkr^^U  ^fiimmds 
^  gfi  dfiia  ctUritM  gtmU^  .  Vis  tnim  hmc^  quant 
interea  )^  nominabo  >  foium  refpicit  pun£ti 
cojusqut  velocitateni  genittm ;  t  maflt  omni« 
fto  pr«rcinclit«  Cum  vero  mottis  acctleratior 
fine  fiuxtt  temporis  ne.cMcipt  qoidtm  poffii|> 
erit  If'  r  s::  C  Faaa.  mu^inqae  diYifion» 
_ 
per  T  obtintbitur  W^  «  *^  ^ 

M9I  'V  m-  <•**«**-*  C$.  ^ctr ) i  ittmni  cKvidtn^ 

io  amba  wfaiiia^  aik|  mt  M.  fitr  ^  st  «^l  fr- 

ftiliter  tuten  /f  »  — t  cr»^«  -r-  (J^  i.txipi% 
.    -  /    .  IV.J 

. '  ■ .  r  / 


IVO  b.  «ff  vk  neceleramx  efl  dirtRe\t  vis  mnrlx^i^ 
moerfi  ue  fneffm%  Qum  in  tnallis  divcr(is  eo  mfltorcm 
^c  opoftet  vtffn  acceleratricem  ^  quo  vis  motrix  ftierit 
major ,  &  mafia  'minor.  In  mafla  caideni  via  aecekra* 
trix  «idciB  el^  fuac.  vk  motrix. 

CapUtllL 

Dc  Con£i£lu  Cojrporum. 

$.  167^  CoHiduntur »  ac  confligoot  cor« 
pora^  quotio^  in  fe  fe  oiutqo-aguDt»  ac  rea* 
gune»  Agunt  yero\  ac  reagunc»  ^uoties  aU 
terum^  ab  aitero  urgetur  ad  mutationem  fia<- 
tus  iui»  quod  fieri  foiet  corporum  impsBu^ 
ikw  jeorttiiaeai  imurfa  1  aut  wcutfiu 

^.  IoS«  Imfiieffmi  corpora,  ii  onum  coo* 
iHigit  alterum  diredioni  fux  objedum*    In^' 
unmM^  qiiorum  unum  impingit  inaiiud  vel  i 

•Qie&eoiy  vei  ad  eandem  partem  motum» 
Jkeutfunt  denique »  ii  unum  impiogitio  aliud 
ad  parte^  oppofitas  motuou 

Scbol.  Mthi  dfinceps  impiuffef  e^rferi^  dicenntry 
iuHaeMi  eenciefet  almiin  (f^i^aeue  dice^oni  Hm  ol^ 
jcdttni;  fnovrr^r^  autetn,  (i  nnum  impinget  in  aiterain 
fci^e^ns  lemim  99^m  md  eaudem  partem.    Qemr^m 

eidcpi%ttificatajecijnlni»  <^«b  ^ 


^«(109.  Cum  de  conflidu  corpprom  a* 
l^ri  fiMcmeodi  liiM  MjTAeta  dora  a  tnoUi^ 

^^. :    ' 


tms»  M.n  elaftica  ab  elafHcis.  Iburs  AvA§ 
quorum  figaraab  alio  iropingente  non  mtt<«, 
tatun  Bl^icA  nominavi ,  quae  fuamec  vi  ni« 
tcintur  recuperare  figuram  amillam  i  vti  ekf« 
tenfionem. 

Cbrffff.  Qotre  fi  corpos  Jsimm  impellit  aliud  itt» 
dem  iurum  ,  nihil  de  vi  ioipellemis  trnpenditar  in 
eUum  efTedu^fli,  h.  e.  in  partium  compreOionem.  Im* 
Jtenditar  autem  in  confliflu  elajticorum. 

ScboL  Agam  primum  de  eorperibos  iarky  tmit 
itt^Haftkki  in.utrisque  ciMifiderabo  imo  impi^um 
edo  ineurfam^     jtio.  4C€urfum, 

^.  I  lO.  Si  €arpuf  durm  impiu^t  in  diud 
dtirism  ^uitfiiHs,  mevmtur  ambo  fo^xonfiiSlum  c$^ 
Uriiatc  commuHi^  i^  caJcm^  Nam  corpus  per« 
coflum  non  movecur  cardius^quam  pci^cution V 
slias  permaneret  conflidus.  Sed  neque  mo^ 
Yecur  velocius,  quia  percutiens  (blum  agicia 
^rcuflum  >  gnatemif  tftud  obed:  iiKui  mocui; 
non  autem  obeft  amplius  ,  fi  eadem  velocita« 
te  feranmr  ambo;  quare  nulla  fiibeft  ratiO|i 
cur  alterum  (eparetur  ab  altero ;  ergo.  lC 
fivincit  iilud  j^xperientia  in  globis  aa  pef fe« 
Ao  duro^  proxime  accedencibuit 

$.111»  Jn  impaSa  mpmrgm  tiltFrH4i 
#aii9fNM{/  d^uMut    ■;  »    Sic  mobile  A^ 

le  «liild  S  i  pmtls  ma(Si  dioi^r  M^  celericaf 

3         toc» 


>  •• 


fjltfl  .MhlL  Csptnlir. 

«iite  confiKtum  C;  alcerius  maflTa  vocetui;  f% 
cctentaserit:^  zero  (  paniturenim  quie^ce- 
re)«  Utriufque  celeritas  poft  i^um  zs  JCm 
Mobile4  unpingens  decemun^t  akerum  qui« 
•fcens  ad  motum ,  eoque  fcnfu  ei  communi* 
cataliquos  celeritacis  gradus^  &  ita  commu- 
ATcat)  ut  pofl:  lAum  amtk>  eadem  ceteritate 
ihoTeanmr  (S.  pr«,^»  (^arein  confli^ti 
celeritas  Cdiuribuenaa  eft  per  mafla^  M^Sitn^ 
pro  ratione  mafTarumi  cum  in  (ingulas  utriu& 
i|ue  maflk  pariicuias  fic  diftribuenda.  Hoc 
aotem  ip(b  celeritas  communis  x  tanto  minor 
efTe  debet  celeritate  priore  C,  quanto  mafor 
ffl  fumma  maflarum  mafTa  unica  corporis  in- 
eurrentis,M.  Habebitur  proinde  harc  prq* 
portio :  M^tn:  M  :=i   C:  x    Fa^a  medio* 

MC 
mm  dividendo  per  primumifiet  *  s:  ■■> 

MoL  A  celeritite  commuat  ritc  inventa  pendet 
fi>l<ftio  miorum  problematum» 

U  Invtnirc  celerMwn  amiffkm  a  corport  impi^ 
gfnte.  Invenietiir  aucem ,  (i  ceieriias  caromunis  poil 
i^laai  fubtrahetur  a  ceieritate  aiue  confli£lum%    Erg<^ 

MC  * 

C  ^   — —— —  dabit  amiflam  celeritatis  qttantitacem  i 
M*i*m 

Siuim  X  voGO.    P^rro  ii  Creducatupad  fraSionem  fub 
enominatore  M+  m  (quod  falva  ^qualitate  (ieri 
ppfTc  nemo  ambtgit ,  nam  i  s  t ;:?  |  ni^  ,  ^^*  ^  ^^^ 

MC+mC 
A«biiur   C  ?;  — —  -    fafta  fublUnitione  cr'4 


2V  $otifiifh  Hitpm^m.  X9% 

jl  «3  «,,«»..„...^.._«^  .    Ciiftiqiieqadtititate$4% 

Itooftcnex,  obi  tantDHi  adeft  dt  pofitivd ,  quantam  de 

w»C       .'    .  ■ 

negttivo ,  le  (e  tolkmt ,  erir  ^  S3  — -•    Ope^ 

Af  +  w 
rttibnif  rite  peraChr  ittdicjam  erit ,  (T  qu^ntitas  celcritt* 
tis  apiiffie  addita  celeritati  coipinuni  poft  coniUfVun^  ?5 

AfC  +  «f  C 
cclcriiitti  ante  confliaum.      Eft  autem  —  — ^-' • 

S  C,  quod  fafta  numeratoris  pcr  dcnoroinatorem  di« 
fifiooe  iiquido  perfpiciecur. 

A\»  Detmniuart  ccmfjnmem  qwmhatm  motm  p9/l 
fmpaRum.  ^.  Quantitas  motus  cA  maffa  dii^  in  c«» 
leritatem ;  quare  ^fumma  niajpirum  ducetur  in  ceteri* 

MC 
latem  communem,  h.  e#  fi      '  ■  ■"  multipiicabiior  pcf 

M+m 
M  +  m  y  baSebitii^  commcinis  qimntltat  motos  ti' 
MMC^MmC    ^. 
I  ii^  .,  >    Si  deniqtic  frafiionis  numcrtfor 

iividctar  per  flenominatorem  ,  repcrietur  quotient  :ss 
MC    M  enim  continctur  itiMMC  pcr  Af  C,  quci^ 
ticntc  ifthoc  multiplicato  per  divirorem  A^+  w,  faSa. 
que  produfii  fubtrafiionc  •  dividcndo  nihil  crit  uitra  ^ 
f  uod  dividatuc» 

GfcS,  Etiam  ante  confliaum  quantitas  motus  :ia 
Jlf  C       Qoare  pcncs  corpora  impingcntia   commuuM 
quamitat  motus  pofi  cofifiiSum  s^   qnantiidsi  mom  ofiia 
tonflidnm. 

ScboL  II  Jureritfiwnnulattpplicwflenumeris.  Fonc 
M  ^  6;  C  si  4;  Mt  sa   a.    bit ^lcritas comma^ 

N         7    ,  nit 


/ 


/^ 


«lue  cenfiKtam  C;  alterius  malTa  TeoHat:  m^ 
cileritas  ertt  =:  zero  (  poniturenitn  qute&e* 
re)«  Utriufque  celericas  poft  i£tam  ;=;  x« 
Klebild4  impingens  decermin^t  alterum  quj« 
•fcens  ad  motuin»  eoqiie  (enfli  ei  communir. 
cataliquos  qeieritatis  gradus^  &  ita  commu- 
Aicat)  ut  poft  lAum  ambo  eadem  ceteritate 
Aoveantur  (  €.  pwc.)  •  Quarc  in  confliAa 
celeritas  CdiUribuenda  eft  pcr  mafla;  M^Sim^ 
pro  ratione  malTarunii  cum  in  fingulas  tnriu(l 
fue  .nui&  pariiculas  fic  diftribueoda.  Hoc  ^ 
Mtem  ip(b  celerkas  communis  x  tanto  ininor 
efTe  debet  celeritate  priore  C>  quanto  major 
•  ^ft  fumma  maflarum  malTa  unica  corporis  in« 
carrentlsrM  Habebitur  proinde  hxc  prq* 
portio :  itf  HE^  m :  Af  :=:   C:  m.    Fa^a  medto* 

MC 
fom  dividendo  per  primofii)fiet  x  s5  ~~— • 

Miiim 

JieiaL  A  cdarittte  comment  rttt  inrceta  ptoAit 
loleito  mioroin  probieniAtufn» 

L  l«i««tirc  peUri$0itm  0miffkm  a  corporf  imfiaf^ 

:  Sfme.    Itiveiiieciir  aucem  ^  fi  ceieriias  coromunis  poil 

ii{|i|ai  fiibtnihettu:  a  ceieritate  aiue  c^nfliflutn»    £rj;9 

C  •«   >^"— ■'  ■■ "  dabit  ami(ram  celerltttis  qttAntitatcwV 
M+m  . 

Sgam  »  voeo.    P#rro  H  Creducatupad  fradiontqa  fub     ^ 
enominatore  M+  tn  (<}uod  &lva  ^quaiftate  iieri 
'  pofli; nemo ambkit ,  nam  t;z  ^i^it^  ^ &c.  ^  obtl» 

MC+mC  ^  * 

Atbiiur  C  »  ■  I   &3a  rttbltiudane  erii 


1 


l»«4    ,  ■ ,  CuiTique  qcKiotitftte)  1% 

iDOgcnex,  obi  taRtnin  adeft  de  pofitivd ,  quantnm  de 

mC       J 
mgativd»  le le tottaiif,  «|ic  if  ^a  '  "  '  •    ^p^ 

Af  +  w 
i^atibnif  rite  peraO»  itidiciam  eric «  fT  qu^ntitaf  celeriti* 
tis  afniffie  addita  celeritati  cof^miini  poll  confliftun^  s^ 
\"                                          MC+mC 
ccleripati  antc  confUdum*      tft  aotera  — ~^-^ • 

m  Cy  qood  fada  numeratoris  per  denominatorem  ii« 
ifiooe  lii)otdo  perrpicierur»  ', 


41  •  Dttmnjnart  tamrnunem  foamltuUm  mom  pfi 
§0fptt&Mm.  'I^«  Quantitas  motus  eA  maffa  dii^  m  c#k 
leritatem ;  quare  ^fumma  niafjkrmn  ducetur  in  ceterii* 

.  MC 

nttm oommunem^  h.  e«  JB  ■■  ■  »'■■    moltiplicabitor  pef 

ilf  *f  »  )  ba^ituf  commonif  qoantitae  mocot  :i4' 

MMC^MmC    ^ 

■  <H:         '^*    Si  deotqoe  frafiionis  nufflotino^ 

Af+f»  > 

iivtdecar  per  denomhiatorem  ,  reperiettir  qoocfcnt  ^ 
MC.    M  enim  eonnnetor  in  MM  C  per  ilf  C,  qtiOP» 
tienfc  iftboc  multiplicfito  per  divirorem  Af+i»,  faOa* 
«oe  prodofit  fobtrafiioBe  «  dividendo  nihil  eric  ultra  , 
fltiOii  CmVi  aaciiM 

\  -  ■ 

Gf^f  £H$im  ante  conftifiom  quantitas  motos  s4 
3lf  C  Qoare  penes  corpora  impingentia  tcmwmui^ 
quttntim  mims  fnfi  em^lMmm  jiH  tpimmisii  mtm  mm 
9onfii^nm. 

5ir(6a/.Xt  jTiTeritferaalafippliarilflenttmeris.  Fono 
Jlf  S3   6;  Cai  4;  m  aa   %.    Srit  feiericas «ontmo* 


t^4  Stiholt  €ap»t1sC 

mC        •  8    •  -         ' 
ItriMtis  •ini(r« ^  aa  —•  a:   u    pcbiqut  com- 

■  .     .3fMC+Af,»»C        i^^  +  ^t* 
Qittius  qn«ntiAi  motitt  —  ~ 


■*M^  £S     <MHto 


•  ^  .  •         •  ^'-    ^ 

..  •  ■    '  ■•     -        •  '531 

5«  112.  /1»  tHcurfkJurffrum  ^fkrka  tml 

mnisM^Mtur  "  ■ »     '    >    PoiTunt  nttnpe  cofw 

por«  incurrentia  {pe<ftar1  ^  tanguam  fi  len« 
ttus  motum  ^  quiefcat , »  &  ceierius  mottim 
fpla  celeritatis  differentia  accedat  (  eft  enim 
f^  Propmiom  Aritbmttka  4  r  d  t=:  la  :  o  )  ; 
pnetur  propoicip  i^giiens  '^  M  ^  m  l 
fy  )k   C  ^  c  :  ^.       Fifto  inediorum   di- 

^ifii  pcr  ^imum  ^tinebiiuf  ^c  sss  ■  ■> 

DefigMt  Verty  .X  celtritttem  communem  | 
quam  (bfam  mafla  im  obVinefec,  fi  quievideti 
Sed  non  quievit ;  neque.  de  celericate  prius 
£abita  quidpiam  decerptutn  fuit;  qiiare  ccle* 
riias  jamantc  habitli  addtnda  tH  ad  ctltfita- 
—  MC^  M^ 

nm  rt ccfls*  Mqittifitaaa  i  Cimma  — --^^ — — — 


y 


#  €  dabit  cclcritatcni  comfnunem  poft  coa- 
fiiifttHn*  Q^^hf it^tcfn  «  rcduGcnda  a^  wn^ 
dem    dcnominatorcnir  JH  Hh  m    obtincbitur 

i^       -  ■■-  •  ■  ■  •'  ■-'  -^  '^st  ■"''  '■•' '  "  '?*'  '•  \na0Ei 

-  i€-t^}ant}V 


•**  ••'. 


ScM  !tenmi*c«fri!t!i  c«lerit«it  «iiintnm!  fvft  hi» 
CHrfiiiii  ftcititcfit  IMatio  pmbletn^tiiin  (e^uentiiim  i 

i,  Ifmvi^rt  u}eYit((tem  amijjkin  iu  c&tphre  fifciir* 
rtynt^  1^>  A  celentite  C  ante  i^hifn  hafoita  fnbtridia. 
fOjr  «elerim  cpmfnums  ]^ft  idufn;  dfiTeientia  d«bit 
mantitatein  ceierkatis  tmlHk  ^  oimtni  jc  vocarc  iibet» 

Omcc  C  >,  -^-^ — ^— .  5*  ik;      P<m:o  fi  Crednectnf 

;     Jiifc+«c 

i^  caadcm  4cnominatorem  M^m^  ficc — • 

MC+mC^  MC^m 
cr^C    Fifta&MSillttoittfit"''*   *  ■     j^«  ■ 

air  ici    C«mfthtndo  ^emiaoi  jper'  omil&ohcii]  ^ipmSf- 

wwi  6  &  toU^miuoi  habebitur  «»  ■'-"'  " 

p  •       •  >■  « 

n.  hmfiift  tehrimtm  ati^i^m  «  c^rp^rty  im 
autli  imurrfhittir*'^  l^.  A  ceieiitate  comtnunt  fubtrt» 
fifttur  celentas  jam  tntcliabita;  diffcientia  «Sabit  cclt»' 

;ftfc+wc 


l^  MktL  Ctpttnt 

'■    ■"       SCK  4V  ;  iDIBidil  ^pMOtfltttibttl 


«k»«a«M«MMa»ii 


le  ft  tollemilMikMptritter  «  «  , 

J^WwWTftfnmFW  «IHPMnHOT  MMIillMIflTi 


MMC*Mm^Mi 

fiiaiAiim  niifliiiiini  fitflott.*''»    <> 


dabit  eofiimQnem  qtiMititihNii  mohii.  J«m  fi  nwne- 
rator  per  detiominfttorem  dKvidetar«  quotiens  obti* 
fiebitor  ilf C  4*  19»  ^  Hak  eft  eommanii  ^uuttltis  motnt 
pofteonflidom; 

CtffilL  Btiftm  ontd  eonflidiim  qiiantitis  motU|  S3 
MC^  m  9.    Rur(bm  ergo  communis  quantitss  motus 
foSt  conAiaum  e:  qoantitati  motua^nte  confliftum. 

|i.  II^.  In  MCttrfa  corpwooi  c^ieriraft 

cottimunii  aBquttur  — — — ,    f^^m  fi  to*^ 

f a  celeritai  relati va  C  if  c  in  ibmmam  mafla* 
diftribuenda  fit,  obtinebit^ur  M  4f  mz  • 
MC^Mc 

C^ig.  u ^      At  enim  corpuf 

M4!^m 
re  alterutrusi  t  fiyo  otrumque  crieritatcja 
prius  habitfiiD Vmittit.  (  Tiribui  oppofitis  mu9 


fQbtr«li«Ada  I  fict  — ^_  ^ 

Ortfft  Si  HCx  «•««,  <«P^  <l«fefc«t  <  •* 

*  ■  '    ■  .  '  * 

t  nafl*  maflk.  &  celerit..  eeleyiwi  W«*;jftr  »• 
ii  mtffie  &it  iretipiroQe.  ut  cempaiW  lm*t  ««t  «  « 
«I  C. 

Seh»\  Hebil»  c^erim»  ««(vawai  «V*  ftdU,  *| 
«ciot  dedocamoi;  fcqaenria  )  ,  .  '^ 

•^     l.  ii,»««r«  ^crimm  -W*,*  ««?»'*  •'*!I!l 

«itftft  ^aB«c«>«itv„  habAiw?  C-  ""JJ"'  * 

MCt«G       3»(K:+«C-MC+ii« 

Bro  CiablUtaendo,  •*"-: — »  ^«'t  j  n  '  .  „  " 

lltfll  /    iw  +  w 

Af+iw  ■ 

stt0M  UmiM  tnm,      Tlh  A4.  eeiecitiwn  comroanej» 
Doft  confliaum  addatur  celerltaa  ant»  c»n^®°?'i.'l** 

M>itav  — — —  Me  e»     Si»e  ■ 

Mt«  ■«+• 

MC+Me  •      ^  i 


\.. 


UL  tiitirmiiimt^  cmnmmm  y>uiii1*»itf 
Y^A  mnfiHtimK       :^.  Gelerita^  eofBouniit  p»ft  cwA* 

AtC^»e 
Hmg^    *■  ■■*    dQCtfctQr  m    (uii^m   niillbtia 

itf-^m    Ohtincttoir  ■  wmp 

JUrAim  $i&i  attmer atoni  pec  <^enoifin>jtftr€m  HpSaam 
coa(urgetquota$MC^  mt%  ^  .      ' 

m 

CorcU^  Penes  corpora  occtsrrentit»  &  offcfi^  A» 
^Sttonitm  confligfncki  eft  qaantkfts  .motitt^ante  copffi* 
fiojo  :=: .  Af  C  7-  /ff  ^.     ^^^  cadfiisi'  cft  j^ft  coii4|» 
&azn^  quc  ante  coafiiStmiu 

^kiplTL   Si  Ivk  wmw  t%fimiti  Kbet  qa«itit«i^ 

tem  Cve  mdtus,  ieii  celeritatts  amiffie»  tut  ac^uiflt^ 

4icatar  mafTa  M  z^  ^  ^   19^  ii   24   celentas  tTz:;.!^'^ 

•f  =3.  }«     Qua  aiethodo  SaguU  rcperirc  ticett  ^  docei^ 

jtatlytieir»  quas  max  dedi,  formobt» 

SMoKA  Plarimt,tc  poMierrtmt  {tne  Ae»reiiiMM 

,  fBidts  veritatibus  deduci  poiTe  tefiis  mtbi  eft  Boshv»» 

tbm  tn  SitppL  L.  IL^ad  fhSofiph.  Sutyatu   qo^em  qut 

.  irolei^coiiraUt»  '^Sgo  brevttttia  cta&  iatenmttere  eogor, 

$i  114«  Jd  ilafiica  acceda  r  Vif  elafiica  ^ 
jgpcatur  vi  comprimimi.    Nam  vi  elafticft  fcfi^Uwr 
cornpreffittni  y.-.jk  Maiginir  \n  com^rimeiis ;  . 
n^aatem  aftioni  aEqualis^  £c  concrarui  reaAi^ 

^t  1 15«  /li  tU^icif  CdftfiS^iinihi  cadcm  ha$ 
htur  vi$  clafiica ;  fiam^  propter  vtin  daftiQam 

«lc^rias  comprimicur  corpus  4(ef am ;  proiiSN 


../ 


dM«8i^fl  ^^tiS^^Stmptt  zs  vi  compriinciU 
tiy^corpora  ebftica  in  coitifliAtt  iimitm  aG« 
i|uir4iiirvim^l«fticam.  ^ 


^"  .J5!f  ll<J.  -iii  C9n§iBu  ct^icorum  M^etur  id 
wiUt  ifTM^miis^  ^mmitur  infiquentis.  Prapc^ 
^W$f  Miin  per  .pompreiliofiam  *  infeqiientif 
impellmir  W^W»  qoa  prios  ffi?tbatar»  HrH 
Siw$\  inrcqqens  pcr  vim  elafticam  prjrce*- 
^cntfe  iihpclHnjf  dircaion^  pri^t  cmrMjir^ 
«qm  impulfio  contraria  direcftfeni  mobiltl 
imminuit  ipGus"teler!rat<5m  }  faAa  vero  jaxti 
^dirca^pnem  aogei;  cclcritatem  j  ergo..  - 

$M  liy.  1n  C9nJH3u  dafiici^mm  imwmntium  • 
§cquiritur  $^cm  cclcritii  relativai  qua  ctyrporapcjt 
ionfit^um  afi  rwjiupt^^  xfua  fuit  anu  conpHum^ 
^ua  corpora  ad  fi* ^ccedcbant.  YiSi  cniip  ^  q^i^ 
confligunc  clajUca  in  fi  fi  incurnntiay  eft  foli 
differentia  viriiim  abfolutarumj  haic  vcro  »• 
^juatur  vis  eUftica  ,  qtia  prior  eorum  vis  cli^ 
ditur;  quare  poft  confliAum  eadcm  habetur 
vis  rclativa.  Uhi  eadem  vt5|  ibi  eadem  wle^ 
irit;^  relativaj^crgo. 


CVoffi  Si  ecloritas  relatit^  caclem  ant^,  qti«  poil 
eonflidiuiH  ;  ctiam  mtncptibus  Usdcm  mains.  candcrm 
cflTe  cportet  motus  qaantltatem  poft  I^am  >  quc  cru 

Schl  t  Tficoremati  bi^ie  Innitunmr  ftqocmla  i  ' 

t  Pmwtiiafi^eceUritatm  rehtkam  ^,  fUAfot 
^mifiiSum  wmdjirlc  rcccdumik    Si»l  m4<&4^,  fkmj 


\: 


A«ni<»;  nmtk  mtntt  iduoi  e^  poft  idui  jr«  Cfl«i 
ftns  rttttirt «  qoa  eorp<Mra  «cMl^ntt  mif:C^  4;  qns 
rece<lont  j»"«  x  (  jT.  Ii6.).  Cqoi  eadem  iit  celcritM 
c)ilHcorDnt  a  (e  recedenciom  „  qa»  fbk  focedenttaai 
(|.  prxd  )  t  habcWar  jr  —  le  a  C—  r«  UrrtfiqM 
iddeneb  x  ( quod  fit  traitciendo  jr  in  pemiti  thihifll 
fub^no  cMiriirM)  erit^s:  «4*0-*  ^«  EftviM 
«nte  c«nfli6liiai  quantiut  oi0ni&  s:  MC+mt;  peft 

ftftBffi  »  ilf  X  +  01  j^  (  V  P^*^  ^i** )  «^  Quere  m^ 
^i^mczA  M  X  +  m^  RorCiin  i  qi4ft  Ja  s  +  Q 
r^  Cy  txlt  flftj^  s;  #ijt>{*faC"-*n>«;  &£bqiie  rol^ 
^ totione  pro  my  orUtur  ilf C*|>  m£  zs.  Mx  +  mx+ mQ 
w^  m  c.  Sl  quaiiticaccs  notae  ftbignocis  (eparabuncor  ^ 
SctMx^mx^  MCi^mG^  mC^mct:^  MC^t 
m  c^  m  C^    Iterum  dividendo  atrmque  pcr  M9 ff^- 

MC»%ih^'^  mC 
^J.  !•  axiom.  4»)  obtmebicur s  »  ■'■    -> 

M^^m 
lAw  cft  celerica&  fnftflsr  M  poft  CQltfliQuou    Invenr^ 
Valore  de  x  nnllo  ncgotio  cruitut  valor  de  y.  '  Eft 
tnim  y^  x^C  ^^  c.    Quare sqqaUa  cqualibuft  (abw 

MC*i  t/»c  -^  «(  C 
HitUendo  fict  y  ss   ■  '  ■•'   ■ ' "  « ■■  -fi  C***  «• 

JLediicendo  C*^  ^  ad  ^ undem  denominatorco»  Af  4;M 

a  Af  C*  2 »i  C'  -4  Af  c  7*  wic 
C^it :  jr  s:        ;        ^  ,  ,■   mV^m»  i  ■  •    Conk 

aAfCijifffc  •*  Mc 

irebcndo  terniinos  6ct»y^  ■■■  '     .    '    *      ■ » '«w » 
^  •         .  Af*f» 

Hatc  cft  fllterius  ma(b  f»  cdcriM  poft  coftfiftum» 

..  ;.  II.  Dturmiuare  teltritatem  mt^pm  «  maffa  M, 
^tr  i^Ur^ta^-  celeritas'<ju$^em  poft  eonflrftum  «  C9« 


ti  €iBjli^  corp$runu  «Ol 

«tleritittt  miflki  6.e*  C  -  — »— ^— —  :a  f* 

JlfC*fifC        MC^mC'^  MC 

fre  C  foWKtaendo  ,  ■■  ""^ict    ^     '^"*^    , 

JNr|.ifi  M^m 

^  tmc^^C        tmC^^mi    - 

Mfii  M«t« 

IIK  Dmi  mkm  mhfimm  mftjfimm  «  m^ 

m^    CritfHit  «iiMHiein  •nte  «ciiifliftiim  UibtrthAtttr  • 
«ihffcitt  foftiWftftlffi  *  aM6wn|ii  «Ht^cclcrititcia 

tMCiiiiie««  Ak 

ifeipifiiim  r  •*  |«M»^    '""■"        •^  *  ■• 

^llfC-il*^»  ^*»iie 


M^m  ■■      '      " 

IV.  JHiivfiiift  mmmhamm  mm^  f^  €9f^thmi 
|)t.  Docannir  fingqm  miflk  i»  raat  celertNces ,  quae 
t  conflidu  habent«    Erit  ^uantitas  iMtos  jin  malTa  M 

MMC^J^ikMmc:  ^  MmC 
•^  '•....       I     T'        '  ■.  \  in  fnaiw  m^ 

M+m  '- 

^iffiMCi  mmc  ^  mMc  -^ 

^  ,  ^      Quantitaa  motoi 

ai  maffix  cglUSimJkmpti  erit  lumma  inarum  quantfti- 
^  MitfCt^i»CtMi«ct«»wc 


n««MV 


p  JtfCff^c,  qood  fi£hi  mineratioris  per  dcnfinuif» 


) 


^dM^  JZ>  Iiv  reperiendt  ciinrmim  qtumttne 
p»  pcpe!^  corpora  non  elafH^ ,  comp^india  ux\  UcQI^ 
OHii^o  enim  deiUMninatore  celeritatu  co^nmujm  exhibcC 
'iHlinem^  quaptitarcifi  m&^%  poH:  conflidtum.  In  cor« 
*poribuf  «laflieit  eoinpendiaria  idbaec  opcrario  io^uifi 
lloa.4;kabei,  cmi  non  fumpJUi:  majfarum  ,m  eommuneffB 
tUquflm  eeleritat^»  Q.^J^ula^  n^ajft  ia  colqri^tfs  j^ 
j)roprM#  4veud«  fint.  .    _   ""--.   .^   .•^  ^ 

Scbol  llt  Verltatcf  noftnollts  hic  Jrfcitdi^ribam^ 
S^s  fac9e  ex  •i^miiiar^  doArilltf  Mrtmnr :  >  - « 

«?      /1.   4S^iffyifrAmtfj^e^i»«|lcf3^ 

in  moffkm^modmn  iugenmn ,  nc  duram  ^  mctus  omnit" 
rib  "ieQt^^  etcfimgmmiF^  (  iaifit;fiMf  et^^Bfi^Qmi^  naflb 
fuppleat  celeritw  pMiQ  iugens}*       Nam  a  conflifln 

llabitiir  cclefitaa  «MiniMi»  m^tp  \    '■■     Cv^  H4«^  • 

Pftno  maflam  ineurrc^ntia  ilf  =^   i« ;  ^^^  cdtefilftqia 

Ai  C . 
C=:'  $i  mafliin  oujeficntis  «  s3  looo^  tri^-..>  a  ,  ..^ 

^^  i^n .        -r  ^  qu«  lam  niodi^  eft  celeritas »  ut  in- 

.  *rtvmi  corgpris  qiucfccmlsj^  aut  rcuftentiaai  oicdii»  lel 
.friftionis  lupewre  haud  pofflit. 


,  Plaufm  imbite  habetur  inft^r  mafl^  omnind^  Su 
gentis ;  quare  fterum  motut  exftingui  dcbet»  fi  irapaft&t 
iiiQdica  eclmtace  in  iftif  d  fiat^ 

!lv    Slf  rtwsJS?  )Wr,  t^  mfii^rim  ferfeBe  ehfiictt, 

tf    eqnatts ,    poJjl['  confiidum    pertmmm   veheiia^t 

tuat.        Sit  cninl  rtafla  impingeus  M  a    4  ;    iftiut 

^elctifai:  C  ^    «.        5Jt  ctiam  mafffa'  quiefc&s  «t 

;;;  4;  «ric  Ifai  icMm  ^  o^   •  V«teetM  ntffariAI 


p-    *^ 


peft  wiflifttt»  s:  ■  ^ »■■■>,■  ■  ts  ~..iii-  34  ^; 

(§.117.  Sefaol.  I. )  •    Alterius  vtro  «mftfiie  «n  vdectMt 
aMCfwi?—  Mc         4i 


^«^«•••MiM 


/.     Mjm  8 

]>ermi:tdri  vclocitates  iuimpaSu  nemo  iiofl  vktet«-«  Ip« 
*JMi  vhane  pertniiti^fenem  ocisiiii>f»rpAre  liett  in  ^^ 
globorum  ebuFneo.rum,  quororo  centrt  iiBt  in'cfldem 
vyoA*;'  TMm  fi  horum  primus  »  csteris  utcunque  fub* 
mttti  in^pingM.^^celetlMte  ^  g]r«l.:i|i  pmfniiim^^i 
«^uriem  y  poft  conAiclum  quieCcent  omnes »  ultimucn 
'fi  ^emo ,  qui  eadem^  celoritate  6«  grad. 'abibit,  qMuiiv* 

irfipiugeus  reQ>e£ltt  praximc^iequemium. 

%Ao*    Sl.M'ific§irrafin  m^  firque  ceteritas  nHiflb 
f»  =3  j  (  reliqua  atttem  pono  eaciem^  qn«  (tipra)»» 
liabebJtur-  celerha"  SDaf&    M  pofk  confliaum    dH 
•AfCtaww?- wC         fl4t4'-'i»4''  .   ^4*        .    ' 

>  ■■       '  '    ■■■■■  !■  ;s;   >"«i  ■'     u    >  N>  ■   s;  ~  cs  }•  E< 

iiliCtw^f-^Mc       4ttift<-«n 

jdterius  nalGB  m  as  ■  ~—  s;  1 1  ^  1  |i 

Mim  S 

'  s3  —  :=$' '  6«    Atqu! '  Ec  itcruBi  ^ermtttanttir  veloeil|« 

^       JDentque  (t  JU  bccurrat  fy»>  eadem  c oofurget  vcloi* 
citas  poft  conflifVuni»  q^  iu  iuQurfu  f^  iirc&io  folum  ' 
ld>iWin  oppofitami  qui^«:itei:iiai  hatiebtfttr  cQmai(i« 
tatio  cclerttattfnu  -  - 


III.  Si  maffit  impnmmet  /uerht  perfette  ttaflic^ 
^  imefutbf,  fmri$megk\M  jam  ijuiifcm  ^  j¥»  pre^ 


•»  V 


r 


9»^        .$$9$m  Qtputm  ' 

hm  f'tfni£lkni$  appcHo  :  qaem  iteruin  cuai 
per{)eiHiicti]o  efficit  direftio  mobilts  pg^  t^ 
pSlunu  In  Fig.  i^.  wlCf  eft  angiilus  ifwidcn^ 
^it.  F  CB  angulas  rtficxi^niu  In  Fig.  r^,' 
^ <j J7 eft  ang^lus  tncidmtke.  UQ  H angulus 
r^rdiionu. 

jr«  120.  CoffttT  ipt$d<mkfn$  ptrptndiculariur 
inciicnt  in  pUnum  durtm  pcfi  ptrcujjionem  qukfiiCm 
Rado  facile  eruetur  e  ii^quencibus«  * 

# 

f.  121»  C«rpMf  ol^ffiy^  intidtmm  pUnum^ 
^9  durum »  ^o/f  ptrcujjimtm  ptrgit  mavtri  pom 
rcMtlt  ad  planum  ^  u  t^  boriz6nuliur.  Nam  fi; 
mobileL  in  A  conftirutum  (  Fig.  13,  )  feratpr 
ifisrfns  pJanum  J)CE  dtre^ione  A  C ,  conctpi 
poteft  urgeri  a  duabus  viribus  confpitantiVbs 
ADy  8c  Af  { §.96. SchoK VI. ) ,  altera  per* 
pendiculaVi  ad  planum/  altera  paralleia  eid^m 
plano  CDE.  Dnm^^niobile  contingit^lanum^ 
viseigis  perpendicularis  A  D  eliditur  per  refi- 
Aentiam  planj^  Vis  autemparailelaiff  ».quia 
jiullum  rcperit  obftaculum  >  tota '  perfeverat  ^ 
'^nKlndeque  i;ram£pr||t.  ^pus  fecmdum  li* 
neamCf^. 

Corott^  Er^D  fiTnoktfo  kicydit)m;|ptoui^  Mifut^^ 
perciiffio  ofeti^ua  iiiki«r  td^  c^mti  vis  totaiis  egilTel 
l^^rpendicuifti^ker^  &  (^vil^sfti  ]>ercuffio  Uh  boc  11)100«-^ 
t(k  dclct^  quo  magis  fuerit  obliqua^  Iftiid  BaKftat 
jioJilalcti  Kiiiic  lO  obfidiOYiibus  eurant  {cdvilo ,  Xni  dx*' 
tt&VQ  globotum  fit  ad  plantim  tnceuitim  cbnrellciidoi* 
fmt,  ^isam«&iti  t^f^  «Q«nSll»t  ^tlWyi^ua^  i^-mdxiiiio 

» 


y&p«ifltcuhivi$^    Scd  &  pontfum ,  mvinm^e  ftfuft6# 

i^ibiis  id  ex^iorattirti  cft  >    feinc  moles  fiiftcntandis  pott-. 
Cttiiil  columms  aptaws  iw  compoiiuiir,  utln  ftcumen  dc 
fitiarit  j  .lic  ricmpe  aquafmri  conrra  illas  crumpentium 
htipctus  admodum  obliqHfit  rcdditur ,   coquc  tp&  mul* 
ttitn  itiJi>ii1tur.    Hlnc  cri«in  haviam  prol-se  m  •cumcu- 
rf)c«nt;     Cerre,  fi  aqu*  incuftant  ili.nAvim,  ni^er  ht*' 
l>etur  percudio  ob  acumeuprone  ;.  (iiTHHtcr  ergo  prora 
^fsomintta  firindens.'  floAjBS  miuoreia  cxpcmur  riilltciv^ 

$.  122\  Mot^  .pvtpmdkuUiriw  incidem  in 
ji^num  fiffrBi  tlafiicHm^  ftfiUtcAdim^vtkckm^  H^ 
dirf^m^  tput^dnmirM  \  iiAm«pianum  perfea« 
cUfticum  perca^ne  corporis  oidentis  com* 
primirur ;  haic^  vero  fui  compreflioni  refiftit 
fonftanter  j  quare  motns  mobilis  (enfim  bn» 
gue(cere^  ac  Tubinde  exftinouf  deber.  Hoc 
.cxilini^  partes  compreffae  figuram  priorera^ 
refumunt  moru  acceleratp  >  eosdem  velocita- 
^s  gradus  (itbeundo ,  ac  prius  motu  reraida» 
to  merant  comprefTa^^  Atqui  Vero  iHud  (ieri 
nequiret  ^  nifi  mobile  perpendiculariter  in« 
^idens  in  planum  elafticum  eandem  vian» 
celeritate  eadem  relegerct»  qua.  adveaerac ; 
ergo. 

Schi.  X^mA'^  ^hduift  nim  dicim^  inde  ctiam 
pro^ri  poreft ,  quod  perfcftc  eiafttoam  iliud  vocemua^ 
cujus  partes  coitipreCne  ftatuiD  prifiititmi  rdfumuT^t  iii^ 
d*m  Vtlodtiitis  ^radibus,  ^uibna  de  ftara  iilo  detnrba» 
tx  funt.  Sedcale:  corpus  in  natura  dari  skn  putOr 
IUud  tamcTi  ccrtum  babco ,  eorpora  qu«^u<^  tttcnmjue 
ix  '"*  «^ideaQtur;^  elafiitt  €&•    %i  maroiocia  ruper^ciea 


'"X . 


vy 


Hfft  Imttm  indnoctiir ,  poft  globi  percqffidoefll 

/  |wrcbu  cireiiliii  iii  et  ^c&riptm,  &,  eo  nMJor  cpini^* 

rebtt»  qtio  inajore  vi  globus  mariiior  ftriet ;  ergo  ia 

iplUntt  percnflionis  m%rm>T  excavetQm  ell  eoroprci&o« 

m jptrtiain  perciiflluiim  ;  ipfi  ttincn  oivitn  |bft  pcr* 

l^  caffionem  non  appiNt,  qnit  putb  permffit  eontiniM 

I  ceitrriine  figoraqi  priorem  re&inpAiiinii» 

f.  129«  Mohih  dU^  imiitm  Ar  ^mmm 
firftBt  eUfiicum  rtfiHn  Ma  ^  «t  4mgfiius  rgkxlmlr 
^audis  fit  m^fik  imidfndt.      Incidtt  niobil« 

tntur  inotos  ilfe ,  (iV«  fnotui  refpofidem  ris 
'   Id  AD^tc^RMmJD plifiMi pefCutiem  ptrf 
rcfiftentiatn  ejusdem  plani  eiftinguetor ,  (ed 
pcr  reftitutionem  partium  in  (fguram  prioreni^ 
acc)uiret  vim  CF  ss  AD  f^f^aec^d.)  •    Vis 
prior  A  F  perfeverat  >  &  (blitaria  orgeret  mo* 
Dileper  CE  zz  AF  ($.iii«)«      Qiiare  com 
corpus  mobile  per  percufllonem  urgeatur  vi^ 
ribus  CF^  8cCE ;  abibit  per  diagonaltm  CB 
( §•  9^- ) •    Sunt  autem  anguli  FCA  ^  tc  FCB 
«quales  ( cum  tota  triangula »  in  quibus  duo 
^   ,      Iiltera  cum  angulo  intercepto  habentur  cqna» 
^  ^  lia  >  (int  ip(a  mutuo  xquaJia  ) ;  ergo* 

CeroU»  Si  molik  imidat  in  planutti  impeffsSe  el§* 
JHcum  ,  etngulus  refissdenk  non  teqmbitur  mguh  inci^ 
dentia.  Tnm  enim  maniente  \i  A  F  non  rocaperfthi-  i 
lar  vis  C  F»  equslis  j4  D^  Oti  pars  tilius  e.  c.  C  F; 
qmire  mDbile  dedintt  ^iagonalem  G  B.  E&  vero  ali» 
gnlHS  FC  B  part  eaagalifC  1 1  ergo. 


$.  124. 


"  ^«124«  Qiix  ir  mim  rtJr^Bxdiqffi^  Jum 
mnii  ftri  filiui  catfa  dicam ;  reliqua  ^^ncacn 
ufum  non  habrat«  Rcfriniiiur  lux  ,  ^m  ra« 
dius  e  medio  alio  in  aliud  penetran^ji^.via  rc- 
Aa  defleait» 

SIcioiL  Mtdhm  hte  ajypcUo  ,  qirid  qaid  laecm 
transmittere  aptimi  eft ;  hinc  in  mediis  habcnda  tant 
^mnia  corpora  ptUueiday  vamum^  atr^  Huai  vitrum 
<Scc.  Satis  indc  patct  dtverGmcm  habcri  mciiiorum. 
Sicut  corpora,  fic  picdia  fiint  alia  aliis  «if^rf^  rcl 
rarhra,  Mercunns  dcnfior  eft  aqua ,  aqoa  a$r«  &c. 
Sicnt  corpora ,  (ic  media  alia  prat  aliis  fnaj^ri  vinmti 
attraSiva  foUtnty  qtts  phrumfut  proportiOfiata  cft  dtH» 
fitan\  excipio  tamcn  corpora  oltofa^  qux  cumjSrpefint 
denfioni,  minorc  tamcn  vi  trahcndi  pbllent|  OC  luccm 
trantmittunt  abfque  notaUili  rt&adione. 

^  125^  tudi  rtfra&iontm  m  Mvtrfi  m^ 
diorum  otiraSiQnt  ptndm  pUriqut  ftmiunt  dafiba^ 
U  Nivtamana  Pbilcfiflfi.  Kede  fentire  viden- 
i«r;  fane  lut  prope  tenuiffimam  caltri  ,  aut 
pri(matis  trigoni  aciem  tranfiensi  conti|iuo* 
teliAa»  quam  inierat »  via  pauUulun^  recedit » 
ac  defleAit.  Qjxas  verQ  opportunior  expltr 
cando  buic  pharnomeno  caufajquam  attraAio? 
In  horam  quidem  (ententia  egregie  demon* 
flrantur  theoremata  lequentia : 

§.  126.  Radiui  lucii  a  tntdio  rariare ptrpifii 
Mfulariitr  incidtm  in  dtnfiui  non  rtfringitur^  nul- 
la  enim  caufa  fubeft  refradionis ;  nempe  duni 
radius  perpendiculariter  incidit  in  medium 
denfius  |  trahitur  a  vicmi^is  ejusdem  me- 

O  .  dii 


' . 


dl2  '  ScSHoir.  Csput  It^. 

S*  1^8*  Radius  huis  oVliqui  incident  e  medio 
icnfiori  in  rsrius  refrinfftur  a  perpcndicuh.  Ra- 
tio  eft  fff  eadem  iJIa  atcra^ione  >  qux  m  nor 
fft  in  r^iorii  quam  denfiori»    Hanc  appliwa. 

Gr«B.  i/rr  /«jc  rffringatmr  ai  pirfcndiculum  p 
Jiin  41  ptrpfndiculo  ^  oijeda  Jetnper  videri  iibent  iilie 
tjfe ,  ubi  revera  noti  funu  Mcns  cnim  fcmpcr  objc 
dorum  cxiftcntiam  rcfert  ad  cxtrcmitatcm  mdii  re£li^ 
qui  rctinam  ioipcllit,  Dum  autcm  lux  rcfringitur  , 
impulfio  fit  per  aliam  lineam  rc6lam  (  diccrc  dcbeUun  : 
pcr  alias  lineas  redlas ) ,  quam  in  qua  objcfia  conttituta 
/unt;  crgo. 

Indc  rcpetcndus  cft  explicatus  pb^nomenorum 
tion  paucorum. 

I.  Sol,  &  Luna  prof  e  horseontem  pnefcront  fi* 
guram  ovalcm,  quia  corum  margincs  inferiorfs  pcr  rc- 
fra£^ioncm  radiorum  denH^rcm  atmofphsram  noflram 
ingrcdicntium  magis  elcvanrur^  quam  fupcriorcs;  hinc 
viciniorcs  apparent. 

II.  Sol,  &  Luna  &pft  fupra  horizontcm  apparcnt, 
cnm  infra  eum  funt ;  quia  radii  folarcs  (ive  a  fble  di* 
reftc  emifli ,  iive  a  luna  rcflexi  fubinde  in  atmofphc- 
ram  nollram  refringuntur. 

III..£adem  aftra  majora  confpiciuntur  fub  ortum, 
quam  J^alras ;  latio  itcrum  cft  in  refraflione  majori , 
qus  habcri  dcbet  (ivc  a  majori  denfitatc  atniofphsrSy 
live  a  majori  obliquitate  radiorum  eminbrum  ,  aut  re« 
flexorum*  ^ 

IV.  Si  in  vafis  vacui  fundo  reponatur  nummus  ar- 
genteus,  non  vidcbitur  a  fpcdatorc  ccrto  quopiam  loco 
confiftcntc.  Affu(a  aqua  continuo  vidcbitur  ;  tum  cnim 
radiii  ex  aqua  in  aercm  cmeroentes  refrin^untur. 

V.  Fac,  parieti  lagenae  virrcae  affigatur  circulus 
chartaccus,  afiula  aqua  non  ciixulus  apparct,fcd  cllypGs. 

♦VI. 


l 


Di  tonjli^u  wrp^rdsfik  2 1 1 

J)6nd{ctitaribus  xiefigno,  fed  ddttiodum  cxiguif^ 
ra^nr  rpatium  attra<5):ionis  CDEF  fic  omnino 
parvum  ;  priusquam  radius  AG  tt  B  defe^a» 
tur  iq  0  propter  vim  atcra^livam  medit  den* 
iiDris  paullulum  derorquebicur  a  via  redia;  9t 
\n  iingijhs  puniiiiis  decorquebitur ,  quamdia 
fp^tium  attradionis  pcrcurrec.  Sic  Vcro  de- 
(cribet  curvam  B  G.  In  G  ccflat  aftio  radium 
defle<aensj  quart  pergic  radius  moveri  pef 
G/^  juxca  diredioncm  m  punifto  /acquifitam» 
^agis  autem  G  H  accedit.ad  perpendiculum» 
qnam BLi  ergo  rcfradio  hoc  cafu  fit  ad  pcr^ 
pcndicttlum» 

CotoU,  tnfertfS  :  refradionem  tion  $eri  in  ip£» 
tr«nfita  mtdii^  fidpauiio  «ntei  dinfn  videlicet  habetut 
attra£lio« 

ScioK  tJtyt6n\ii  titn  {le  detti6ti{h>af  t  Corifotuiti 
attraftio  (eqQitor  ratiohem  direflain  madarum  /  quare 
tadius  lucis  ab  atfre  in  vicrum  dclatus  fortius  trahitui>  % 
Vitro^  quam  ab  a<!re  ;  &  cohtra  d  vitro  in  agrem  delii« 
tns  mitiUs  ab  at<re  tr^hitur,  quam  a  Vitro  (  eft  enim  vi- 
trnm  ictc  defifiu^)  «  ,Ctim  lukvitrUm  ingreditur^ 
augetur  perpendicuUris  ejusdem  moVuSj  qui  ex  adVerib* 
minuitur^  cum  lux  a  vitro  defeitur  in  aarem  (  e(l 
tnim  motus  attradionls  motus  verdis  centrum  >  ac 
})roinde  perp<mdicularis  )  .  Debet  ergo  radius  ex  aSre 
^Uique  inciaent  itl  viti^um  refringi  ad  perpcndicdlum  , 
&  e  vitro  incidens  in  aerem  lefrlngi  a  perpendiculo* 
(erpendicuiariterineidens  nunqUsim  refringitur,  quanta» 
cunqucfit  medii  denfitas  ^  fola  e)us  celeritas  augeri  debet^ 
fi  t  m  aio  rariore  inddit  iti  denfius*  Iftud  quotidiana 
itocemv.r  ixpericntiai 


o  %         <  §.us. 


atz         "  Sc8iQ  U.  Csput  W. 

§•  1^8*  Radhis  buu  Mifu§  incidins  $  medio 
Jknfiori  in  rsrius  nfrin^itur  a  pcrftndicuh.     Ra« 
110  eft  tff  eadem  iila  attra^iDoe ,  qu«  m  nor  - 
ttt  io  ri^ioriy  quam  deofioru    Hanc  appliwa. 

Ortfi.  Sivt  fux  rtfringnur  ud  pirftniiculum  ^ 
/W  u  pcrpfudiculo  ^  oijt^a  Jrmpcr  videri  debtut  iilic 
cffe  t  ubi  revera  non  fuia.  Mens  aiiro  (emper  objc^ 
doruoi  cxiftentiam  refcrt  ad  extretniratein  radii  ic€i\^ 
qui  retinam  ioipellit.  Dum  autem  lox  refringitur  , 
smpulfio  (it  per  abam  lincam  re£iam  (  dicere  icbebun  : 
I>er  aliaa  lincasrtfias),  qaam  in  qoa  objc&t  conltituta 
funt;  crgo. 

Indc  rcpetendus  cft .  cxplicatns  pbraomcnorum 
sion  paucornm* 

I.  Sol>  &  Lnna  prof  e  borioontcm  pntfcrtint  & 
gnram  ovalcm^  quia  corum  margincs  inferiorcs  per  re* 
fradionem  radioxunr  denii^rcn^  atmofphcram  noftram 
ingredicmium  magis  elcvantury  quam  fuperiores  ;  hinc 
viciniqres  apparent. 

.  IL  Soly  &  Luna  &pc  fupra  horizQntem  apparent, 
cnm  infra  eum  (unt ;  quia  radii  folares  (ive  a  fole  di« 
rcftc  cmifE  ,  iivc  a  luna  rcflexi  fubinde  in  atmofphtf- 
ram  noftram  rcfringuntur. 

IlI.|Eadem  aftra  majora  conlpiciuntur  fub  ortumi 
quam  !|a1ras  ;  latio  iterum  eft  in  refraftione  majori , 
qux  haberi  debet  (ivc  a  ma)ori  denfitate  atmofphsrSy 
nvc  a  majori  obliquitate  radiorum  cmiflbrum  ,  aut  rc- 
flcxorum*  ■  '      % 

IV.  Si  in  vafis  vacui  fundo  reponaturnummus  ar* 
gentcus,  non  vidcbitur  a  fpedbtore  cecto  quapiam  ioco 
confiftente.  Affufa  aqua  cqntinuo  vidcbltur  ;  tum  enim 
radiii  cx  aqua  in  aerem  croeroentes  rcfringuntur. 
'  V.  Fac,  parieti  lagens  vitres  affigatur  circulas 
chartaccus^afluia  aqua  non  circuius  apparet|(ed  cilypfis* 

•VL 


f 


VI.  Rcihi  ptrs  climidU  a^ais  immttfk  altior^j  tfy« 
pflr<t ,  qttam  iit.  Etiamque  fraOt  jodicatur.  Sed  ^i^ 
caufi  eft  rcirtdio« 

Scbbh  Refradioiie»  roltdornm  oppofitas  (eqminttic 
teges,  i^ani  L  Sdida  €  mtdt9  ramrt  in  i^fim  delau 
rrfringtmtur  a  ptrpiudtcnh.  II.  E  fhidi^"  den/hre  m 
rarm  incidentia  rejri^jfftnmr  ad  perpendiculutn.  Co|i» 
trariom  obtiiiet  in  Isce.  Sed  non  iftud  miibor  r  fi>lidsi 
inpventar  in  medio^feparanda  medii  partes^  ac  divjden* 
^Ot  Lux/movetur  io  medio  quovis  poros  iUius  per* 
vadendo;  iieri  crgo  debet»  m  fbiida  drmotu  fiio  qui^* 
|)iam  amit  ant^  cum  a  rariori  medio  in  denfios  iilabon* 
fbr,  dum  iatcrei  locis  motas  eademjia  «ircamflimti 
ittgbtuer»         * 

Caput  V. 

t)e  motu  per  machinas  fimplices. 

\  ^S*  129*  fi/Uehinm^\cim\x$j  quidqnid  (ea 
viriuiD  ^  feu  remports  compendio  morum  pro- 
dactr,  3cientia  virium,  vel  temporis  cooir 
pendio  aliquid  niovendt  iUkcift^iiiVtf  audir, 

SchoL  Omnis  fere  machinarum  genera  revocantur 
eul  veUetn^  &  flatfum,  incUnatum.  Dc  ais  poftea  ;  nam 
licius  defiiiitiooes  neceflarias  edootabo* 

$•  IJO.  P$utuU  eft^  quidquid  tnoiram 

groducit;  qaidqaid  moveuir  >  vel  morui  red* 
itfponduf  nominarur.    A^o  p.otenti^i  vel 
pooaeris  tmmmnm  audir. 

O  3  *  Cer^II, 


) 


k    t 


9       SI4  ScffhlT,  CaputV. 

...  C^roJJ.  Etiaoi  ponH"  altcrnni  in  altoro  fibl  roi«« 
nexo  inotnm  .  oducere  potefl,  qufitenus  vi  gravit^rta 
,  CokX  dzCccvidXx ,  vel  defcendere  ntticur  ;  pourrt  itaqnit 
fottJuf  f^teufla  Jubftmii,  «rCim  eundem  effe^^um  pr^ltet^ 
qaem  potwtia.  Jam  perinde  erit,  fivc  pQtentU  CHtU 
pondcr^  Conftr«or,  £yq  pondera  intcr  fc 

5.  131.  ^quilibriume^  apqualltas  virium^ 
HinQ  centrum  4^HiMrii  punftum  illud  dicitar, 
cujus  mota  impe^ito  omnis  w^ffk  imtnota 
«wnet ,  &  circa  ipriun  cQnverti  non  poteft^ 
.Quare  (i  e  pund:o  ho^  ruQineat|ir>  veUufpeiv 
datur  mafTa,  ^ur  mafrarum  ©pe  virg«  cajuSr 
dam  rigida?  cennexarum  Iferies  ^    nulla  pars 

potiuf  deftendcrc  p«wft|  v? l  efccnderc,  queoi 
atcera, 

SoiQLL  C^ntram  ?«eqn})ibru  al^id  cft  tn  m^jQi 
flutvis  foUtaric  fumpta,  aliud  in  maffil  fUiribus  coll^ 
^im  (umptis ;  primam  paflim  emtrum  gravitaw  di* 
cinir,  alfcrum  ^««n^/tt»  gr4W4<i9««f ,  vel  earmnni^  cen* 
frum grayit^t^,  '  Primum  in  ipft  mafla  reperltur,  aJw 
Turi^  plerunKjue  e^tra  maflas  in  virga  rigida  ipaflS^i 
«onne£lcnt§.  ,  IJtricjiie  convenit  <i^ta  definitio, 

'^chol.fl,  Centrum  figurap  ,  (cu 'magnitudinif , .% 
centro  ^quiiibrii  ^"  five  graVitatis  diftingiienduin  eft* 
Sit  "globi  aRcnjus  iiemirph*rium  unnm  fcrrcnnf ,  flltt» 
rum  ligneum.  Quomodo  tn  fphsrfs  omnibus ,  flo  i^  ( 
globo  ilJo  centrum  figurar  cft  puuftum  illud,  a  qiTO  om» 
tita  ftpcrficiei  punaa  iiftant  «eq^atiter  ;''  at  nqn  idcin 
punftmn  eft  cenrrum  gravitatis:  .Faa,  e  ccntro  illo  fn» 
ip^ndaHir,  aiir  fuftincarur  giobiis  ,  f  r^val^bit  jiars  fcCf 

rca  Qb  majorcm  piaflam,        ,    . 


Sd$L  Ili,  Qiicmadmodum  mechaDxj;e  prifmaris, 
^ut  iicici  ciiji)svis  adminloulo  centrum  squilibrii  repe* 
jriatur,  vulgo  notum  cft.  Qucmadmodum  Philofbphice 
detcrminctur  commvine  ccnti um  grayitati* ,  daliittheo- 

§*  132*  PcnJeray  vel  pet^itU  funt  in  aquiU* 
hrioy  fi  MOfnenta  a^ualia  funu  ^  Tum  enim  hi* 
b^tiir  2;qua)itds  di^ionum,  proincfe  &  virium 

{§.$9,     &     104.    )♦  ' 

CoroS»  I.  Virium ,  tc  momentoram  menfutft^^ft 
niaCra  du^i^  ih  c^Uriutein  iniiialetn ,  h.  e.  quam  habe- 
rtt  corpus,.  fi  moveri  incipcrct ;  quare  fi  AfC  ^  mc  ^ 
j^ondera»  vel  potentis  fimt  in  jipquilibri^* 

CoroUi  11*  Si  r  =  ^ ,  cclcritarc»  fiint  \n  rationf 
«Urcfia  ^ipanorjam  ;  feu ;  fft  C;  c  :=:  S;  s^  £i^go  etiam 
4  JUS'':^  mSf,  potcmix  funt  in  squilibrio. 

.  (Tpr^i^*  III.  Si  M  C  =;  «1  c,  potentia ,  &  pondui 
iuni;  in  a?quilibrio,  b.  e.  potentia  fiilkntat  pondus;  ut 
frgo  pond^s  de  )oco  fyo  dimoveatur,  debet  momentum 
por^ntiz  exaugeri»  MQinentum  potenti^  yqcq  m^* 
,Sspe  autem  nequit  exaugeri  mafia  potentiic  ;  erg;o  ce- 
}eritas  majdr  pgrentic  ^oncilLanda  c(l.  Cbnctliatur  lA 
Vcftp,  fi  mjigis  diftat  potcntia  ab  hypomochlio,  quam 
dd  fulteiuationcm  pondcris  rcfjqirltuff 

^.  13J*  Inde  fluit  theorema  totiu5  me^  ' 
chflnicar  prinecps  ;  PonJera,  ^  potentia  funtin 
itquilibrio ,  fi  fuerint  in  rationt  repproca  celcritor 
tuniy  v$l  Jpatiorum  ptrcurforuvu  Snnt  enim  in  " 
apquilibrip,  fiMC=  mc  (§. prjc.  ) .  Qemi- 
na\h«c  FaAa^qitatta  folvendo  in  proportia- 
ncm  ob^inebkttr^ll :  w  =:  e:  C»  Idcm  eflde 
fp«iis,  04^  Scbol 


\^ 


i 

\ 


'  /. 


SchK  Voco  aatein  pondut  unum  M;  dtcrtttn  m^ 
pfiotis  celeritatcoi  C,  pofterioris  e.  OeiAceps  potei^ 
tiaia  per  p  exprirotin»  pondos  per  P.  . 

^.  1^4«  FiSis  eft  pertici  rigida,  &  in« 
flexilisi  gravitams   8c  inerti^  expers  ^  uno 
iui  pundo  innixa  fulcro  imiDpbili  (  quod  tfH 
fmocblicn  dicitur  ) ,  cirm  quod  moveri  pomc» 
Triplex  eft  :  vel  eniin  hypomoch]ion  fitani 
eft  inier  dues  extremitates ,  quibus  applicatur 
petentiay  Cc  pondas;  &  dtcttur  vi^  bcterc* 
drcmus  (quia  fi  moveatur  circa  fulcrum  niiimt 
txtremitates  ejusdem  motu  contrarfo  fisrua^^ 
tur);  vel  pondus  confiituttur  inter  hypomoi* 
chlien  ,  &  potentiam»  &  dicitur  vcBu  komo^ 
dromus  imiffnmsi  vel  denique  potentia  inter 
hypomochlion ,  &   pondus  ;   nominatufque 
hmodrmus  zdi  gcntris  i  aut  vsHis  JimfU$i$ir. 

SeM.  Perrici  rigida  gravleatis  expers  in  rerum 
natnra  non  datur ;  ac  a  Mechanicts  theoris  caqfa  tov^ 
cipitur  gravitate  omni  defticnta^  Qnare »  <}ood  theoriil 
docec,  in  praxi  non  omnimode  obtinetun  Sed  difcri» 
.  men  fi^pe  modicuin  eft.  Qua  tamen  ratione  onine  er« 
randi  periculum ,  quod  ex  negle^la  veftis  gravitate  cn^*» 
fci  pocefti  fif  avertendum»  paucis  docebo  infra« 

§.  I5J.  Tbecria  veSlis  Ge  habet:  Pcndur, 
'  ^,  ppieniiojunt  in  aquihbric ,  fi  fuerint  in  ratione 
§fMtimm^mM  Jin^^tiM^^f^  ^j  iypomccbl'-     ^••'  ^'"^'^ 

ui  pondus  P  ap 
.  ^  —  ,  hypomocblion  «..  ,.- 

wit  pot^ntia  sd  pondusi  ut  diftaotia  pondcrif 

ib 


tU  €$f^U&u  tcrparwn.  %  17 

ab  hypomochlto  addifkntiam  potentiil,  fi- 
ve:fi  pi  Pzz  AC:  BC,  eTitP4C:zpBC 
(  nam  fji^fum  mediorum  &c. )  .  Fft  verb  ?it  C 
fnomenrum  ponderis,  8c  pBC  momentum  po« 
tencije ;  e  go  momentum  ponderis  s:  momenr 
to  potentije;  cotifecucive  poccntia  8c  pandas 
iiint  in  squiiibrio, 

^SchoL  L  Sed  oftendenduni  eft  t  momentttm  p^n* 
derls  defignari  ^er^PACy  porentue  per  pfiC  Sic  olten* 
ido :  f  defignat  jmiiffkm  ponderis :  p  miflam  pdtcnttat. 
jtC  exprimtt  veiocitatem  pondcris,  SCvetoeitttem/po- 
fenti^e;  natn  conciptator  veAli  dimoveri  de  loeo  iuo» 
ut  reniat  ad  (itum  a6\  eodem  tempore,.  qoo  potentit 
tic{cribit  areum  Bt^  pondus  de(cr3iet  arcum  j4b»  Staa 
rero  arcus  radiis  fiiis  proporttonales,  qutre  erit  j4at 
fii  =s  ^Ct  BC,  ^Arcus,  (eutpatiteodem  tempore  de« 
jferipta  iunt  urcelerintes;  ttg9  \A$  t  JS^ficut  Ccele* 
Yiras  ponderis  ad  $  celeritatefli  pocentie ;  proindeque 
«tiani  C  :  c  s  AC  :  BC(%.  i.  axlom.  IV.  CoroU. )« 
}foe  autem  iplb  C  s:  /^Q  &  ^  ss  JSC;  tc  propteret 
«tiam  P/iC  s:  AK*,  qood  cft  mometitom  pondcris ,  & 
^JSC  ^  mcp  qvtad  eft  momcntum  potentist 

Schffi.  U.  Eadem  &  tfaeoria ,  &  demonftrttio  ob* 
liiiet  in  vf  ^  iiom^omo  cujostufiquc  gencris; 

€cr$lL  X  Poodus,  flt  potentia  etiam  fnnt  in^qni- 
librio»  fi  iiitrint  in  ricioiie  reciproca  (patiorufif  confi- 
ciendoruia.. 

Cor^n.  tt.  Qutt  veftis  ope  ma^us  pend^s  attollen* 
dom  eft  per  minorem  potentiam,  debet  potcntia  minor 
•ppiicari  bracfiio  viftit  majoriy  pondos  ma/us  minori. 
<2ao  longtus  procurrct  diftantit  potentic  tb  hypomoch* 
ii9|  fao9  ficilior  •fii  ponderis  eujos^ue  dimocio. 


I. 


Mh^L  IIL  Prifira  h«£  theoria  \t€A%  iea  proportio« 
net.  p.  I--P  p|.  //C  t  .^1S  non  diriicilis  «rit  foludd  fc* 
qi^p^uto  probUmatum» 

I.  T>ato  v^^e,  loco  fypomBchm,  E^  potentia  invetiU 
f  e  ^omiut  fafliiiendum^  aut  elevandtim ,  i\x\o&  x  vocabo« 
Sit  ircSlis  AB^    is  pc^*,  bypoiDoclilion  eo  lAiruamr 
eo  loco  ut  ^Cs?  4.  i9C=:  i^^  4::*  %.     S  c  deraqijf 
potentia   =^   50,  iive  capax  attollere  libras  sa     Qi  ia 
/r  •  ^F^v^-^AC^t  BC*y  crit  '50  :  x  ss  4  :  ^;  .'latirc  4  » 
scs   400  C^^uni  fa&mj$  fttedhrum    ^c.)  utri  q~^e  divi? 
dendo  pcr  4  obtincbitur  «' s:    100.  .     Qqiro  ppnduf 
loo  libr.  hoe  caA  fuftincri  potcU  a  50.    ,Si  -^aridum 
£(V,  «ogratar  diikntia  poteHtts ;  lcvabitur  pondps.  '  Aii| 
fic  operantur.,     Iticontr  proportioncm  (equentctn  14/ 
1  s  50  1  y.     Quarlus  gcomctrice  proponi^nalis  ia\ 
pondus  ruftincndutn,    Hcji  c^dcQ]  cft»   •  . 

•  * 

II.  DariV  t;#fff  :=:  tft,  hypamocblio  xA  Hipra  ponJar$ 
£:;  loo  invenffe  fotemiamjtiftiiieudoponderifatemy  qu4 
iurum  x^  dicetur.  Dato  bypomocbiio  datur  hoc  ipib 
diftanrta  ponderis,  ^  potentije  ab  CQdem.bypomocbito» 
ConAituaiur  hypomochiioa  in  Cy.  pundo  diftaul^  4  p€» 
dcs  ab  -^.  Erit  .-^Cz:-  4;  BC s^  %%\^  4.  ^  %.  %i, 
tbcorit  vcSis  habcfur  5  :  <P=5  /IC  :  BC\  (ive  a:  :  100 

-400 
;s  4  :  8*    Proinde  8  *  =«  40o,.&x  :;:  ■  ^-^v   5::  50, 

$/  volcs  dic  f  pcr  mc  licet  )8  «  4  =3  -iod  s  «•.      Erjf 
^ienuo  quartus  Gcomet.  proportionatis^ ::::  f o. 

III.  0^4  losigittfdijtf  voBif  =^..l4(y  pmider^r^  100, 
Vf  potetitiaT^  50  deterviifiare^  quo  loco  fl^ti/evdumbyfti» 
mochlioH.  Jjxjiiircad^  priinum  dillantia  poudciis,  tuiti 
etiam  potentix  db  bypPinochlio.  *  Prior  cllcatur  x,  pQ- 
tciit  flUcra  deiig^wri  pci:  xa.-^  x.  tJcvoccri\^r  proppi;- 
rio^  ;  fsJ  AC  ^'  BC.'  J-itteriV  valorcm  fuuiu  fuljfti- 


■v 


f 


tuendo  fiert  50  t  100  =:  jc  t  i»  —  #;  preindc  i< 
*-  ='600  —  50  X  {fa^um  cnim  f;/tf//ior«wi  £^r, )  cogr 
tps  a))  incognUjj  (iparando  obtinebitur  X50  #  :;;s  6c< 


600    ^      ^ 


Faflti  utrinqiic  divifipnc  pcr  150,  cWtx  si 

150"        I 
s::  4*     Hxc  quidem  Qftdiflanila  pondcrisab  hypdmocl 

lio.     ErgO  difhntiii  pottMuis  23    la-^»   4'=S   S.     AI 

liac   proportione  inira   defiAiunt  locom    hypomocbli: 

ut  fuifima  potemiay^ ponderis  {  aiit  diiorum  ponderurt' 

t^d  vetfitn    totum  s  Jtc  pqndiit  alterutrum   ad  di/iaf$ciai 

fuamab  bypom^chUq,     In  cafu  no{h*o  150  1  19;^  iQO 

Scb^h  JV.  Libra  {  alias  Hlancem  ^icimus  )  eft  vi 
&is  beteradronH  Jpecies.      Adhibccur  ckaminanda:  por 
derum  sequaiitati ;  hinc  brachiis  oranino  d^quaUbus  ii: 
ftrut  dcber.     E^iimvcro  in  vedc  quovis,  cujus  opc  poii 
derom  ^qualitas  inquirUur,  pondcra  iAmbd  (  vkm  aUc 
xom  vice  potcntis  fungitar  >  Qxni  in  ratioi>e  rcciproc 
diftantiarum.      QoaFC  fi  pondiis^quari  dch^t  ponderi 
etiam  diftanria  diftanrix  squetur,  ncccfle  cit,     Si  bni 
cbia  non  ad  omnem  amuflim  ^equalia  fant,  dolofa   c 
libra.     Sed  dolom  occuitare  folcnt  nundinatorcs  felT 
tni:  brachip  lcviori  lanccm  graviorem,  huidfnapondi! 
|n|tciendo»  non  merces.     Flt  tmo,  ot  minu»  iincei  a  hi 
btfitnr  libra,  quantnmlibet  bratrhia  Hnt  omnino  ^quali 
ii  lanccs  cum  funiculis  non    prorfus  sqniponderen 
Scd  tam  hoc,  quam  alia  librre  vitia  detegi  poninit, 
f  tirdera  }ancibus  adjcAa*  peFmurari   jubeas*  •  *    Si  fa£  1 
t^^mutfltionc  Corpora ,  ut  p'f  ius ,  «quiponderahr,  r 
,piorata  habcbitor  librac  finceritas  *,  fin  minos  r  manif 
fta  erit  fraus,  ac  doius^     Porro  quantitatem  doli  iic  c 
gnofceSjfi  rcm  fupcr  iance  una  ponderataro,  iiidcm  i 
pcr  alterapoadcrari  jubeas,&  notata  utrinque  pendc 

Id  If  (f  ducas,  t^m  CH  h^o  radictsn  ^iudfAum  extr 

has, 


baSy  de|irdicDdef  finceram  rei  pondcrmdx  gnnritateiiB  ^ 
promdc  4c  frandem. 

ScM.  K  Stgura  RomMu^  ctiim  vrAi/  bmroJra^ 
pms  cft,  nt  libn.  In  boc  A  ilbi  difocpa',  ^qnod  bnu 
diiis.  conftet  ojagnirndine  insqaalibns,  in  partcs  «qoa* 
lcs  diftin£lif ;  icd  taincn  brachia  «qnilibrare  debeot. 
Jogo  ftaterx  nonnalitcr  infigitur  lingaula  iinfoobiliSy 
Ua  txdmeu ;  (ic  inftrudom  jugnm  trutins  inferitnr. 
LinguuU  intra  tmtinam  latcns  xquilibritatem  defignat ; 
ii  e  trutina  dimorebicary  inque  partcm  alteruTam  de« 
clinabi^,  (ublatx  aequtllbritaris  indicium  eft.  Ope  fta* 
tersc  hnjas  corporam  maxime  diflrercntium  pondus  exa* 
Ihtnari,  ac  (aftineri  potcft  pondere  unico;  nam  proat 
pohdns  illud  modicum  ( quod  brachio  longiori  appen- 
ditur)  inagiSy  minusre  removebitur  ab  hypomochUo; 
fic  plane  cam  majori  minorive  pondere  aquiiibrabity 
cnm  pondera  xquilibranda  fint  in  rationc  ini^erfii  diftao* 
tianim# 

ScyL  VI»  In  firfieibm  viderc  cft  dapliccm  to» 
Aem  tmroirattmm.  Pro  fouutia  ibnt  gemini  digttt, 
quibus  gcmina  forficum  brachia  reguntur.  Jfon  h«  cft 
in  re  (cindenda.  .HypomocUiou  clavss  eft  vedes  afn- 
bos  conjongens»  Hinc  forficcs  fabrts  caldariis,  aur  la- 
minariis  propric,  acies  babent  pleramqae  cortas,  reU- 
qua  vero  brachia  ntcunque  longa ;  quo  qdidem  pado 
ftcite  potcntia  modica  reliftchtiam  quamijbct  roperaus 
poteft. .  Idtm  fit  defirdpituSy  volJiBu^  aliisque  id  ge- 
fios  inftrameiitis. 

Scbol^  Vlh  Iteram  iu  molis  aquaticis  vificur  ima- 
go  veBHm  io$erodromorutn$  Pro  potousia  haberi  po- 
teft  aqua  ad  cxrrcmitatem  radiorum  frota  rmxima  dt^ 
Iflpfi.  Pro  fttndo  fifito  tocus  r otas  illius  axis.  Pro  poth 
ders  parva  Imorior  rota,  quae  tantam  molx  mocioneqi 
cofflmunicdt^  quantam  nbaxCyfiir^  cjriindro  i^ots  roajo« 
ri  inferto  Tor tiia  «(b 

/       '  ScLol 


• 


Di  ttfnjUBu  €orpf>ruffn  ftM 

^chol  Vlll,  Ad  eosdem  vctUs  revocandi  funt  re- 

ini  navigantl^iriK     Founfia  eft  in  manii  exrremo  unitf* 

f  xdr    ,  Pondus  xtm\  dimidium   manui  alt^rl  affixum* 

HypomMli  viees  obtt  aicerum  rcmi  cxtrcmum  comrA 

^aquas  agitatumy  casque  rcmovens. 

ScboL  IX.  Macbifue  coimnokndis  fahU  Arabicis  ap* 
tat^  dicl  pt^dunt  vi&isbitcrodrotnus.  Ettam  in  iftic 
*inanus  cochleat,  vcl  potkis  axis  manubrio  applicata,  cft 
fro  poteiitia,  Fabic  commolcndse  pro  foftkere.  Axi$ 
cylindri  |KrpcndicuUris ,  cui  nux  adhsrct  ^  fro  bypo* 
tnocblio, »  Quid  mirum,  (i  fab«  illar  nulk>  propc  labore 
impcnro  commoluntur?  fcilicct:  magis  ab  axc  cylin- 
4ri  diftat  manus  ^  q^uam^  quas  rccenfui|ya£^« 

ScboL  X»  Cttltri  fbarffUKOfaorum  t  piftonm  Vt. 
tina  fui  extrcmitatc  tabulx  tffixi  Gktit  vehet  bomodromi. 
Fotentia  eft  in  manibu»  m^nubrio  (qnod  voeant)  «p* 

{h'catis*    Fonius  cft  rci  difiectnda.     HyfotHocUi^  l^- 
etur  -in  punfto  fixo,  circt  quod  cultri  aguntur.     * 

,  SthoU  XL  Innui  Hiprt :  in  veQt  qtsavis  etiam  gra* 
vitatit  rattouem  habeniam  ejje^  Rc&nc  peraguur:  fic 
v|£lis  ACB  (iig.  15«  )  (cx  pedcs  longus,  cujus  extre- 
tnittti  ji  tppendtmr  poadus  lihrtrum  aoo;  extrcmi- 
tttiS  xoQf  Lil^rstoo.  diftent  daos  pedcs;  xooqtu- 
tuor  pedcs  a  pundo  fixo  C  Pcnique  vc£lis  ACB  ap. 
fttni^t  libi^as  XI,  Jam  fic  opcrarc:  L  Transferpon- 
dus  vcdis  tptius  in  ejusdcm  ccntmm  grtvitatis ,  quod 
€4fH  i/to  crit  dimidium  vcfliSy  five  diftabit  pedem  amifn 
t  puinclo  fixo  C       II.  Incatur  proportio  icqiiens :  ut 

'-  iifimttia  pmderis  in  A  locati  a  fmiSo  fix9^  C  tA  difian» 
tjdm  centri  grMvitutu  ab  eodem  fun8o  C  ;  Si<:  gravitns 
t^ius  veSit  td  jttartum  terminum^  qui^qiiantum  dc  «. 

.  quilibraado  pondcre  demcndum  fit,  planiflime  sndica- 

-.  .  .  xa    ' 

bit.    Brcviteri  fiatbcc proportio  s  M  s  121  —  :r 

% 

'  V     "  -  ^  6 


6.    QQafe  ibo  pondo  cotitinebum  in  cquiUtiHeae^  alin 
194*  pondo.  '*f' 

Sitidem  vcdis /yCi?  ti.  pedes  longas,  fed  14«  ii* 
bms  appendens.  Pondui^  in  J^ss  300;  in  £  s:  loo. 
Dillsnti.a  prioris  flb  hypomochlio  s:  3i  poiterioris  =::  9« 
Si  eodcm,  qtio  antc,  modo  operaberis,  comp^ries  Iibrds 
S4.  fl  -^od*  rupputandas  cflb,  ut  «qnUibrent  lod  flliis« 
Cur  vero  ?  quia  Centmm  gravitatt^  ih  veOc  AC8  apqoe 
diilabit  a  pun£lo  fixo  C,  ac  potldus  )0o.  librarum  &il 
eodcm  pon^o  C» 

ScboL  XII.  Ve^is  coinpoJiTiu  macbina  igft  conl^ns 
plurlbus  ve£libus  ita  iibi  conjugatis,  ut  ve^is  hniu^  ex« 
tremitas  M^tremicati  altcrius  incumbat.  Haberar  f^ru 
fhXy  tripleXy  qtiodrnpUx  ^c^  prout  duf^  tres^  quntU^t 
vefites  coinponuntur*  Ejus  tbeoria  fic  h^bet;  Foten^ 
ttA^  £?  pondm  fwit^  in  ^tquilibrio^  fi  fnerint  recifroce  ut 
faBumex  difiatttiif  minoriitu  adfaQufn  ex  dijiantiif  mc^ 
jorijais.  Sumo  ve^cni  triplicem.  In  fingulis  dillancia 
p«n«[cris  ab  hypomochiio  =;  9;  difiantia  potcnrix  St 
9i  Eritp  t  P«3  »7  »  ^29*  Colliges;  admirando  vi« 
rium  compendlo  grandia  onera  attoIJi  poiie,  fi  vcdel  cu* 

mulentuf*  .      '     . 

■»  • 

§*.  1^6*  JVff^i/wdicuuf  orbis  foHdas,Vct 
rotulacircd  «em  vblubilis,  habens  in  circutn* 
ferentia  extima  alveum  excavatum ,  cui  lorci 
funis,  yel  catena  inferi  poflint,  Dupkx  efti 
fixs^  quas  in  c^ntro  fai  ita  figitur,  uc  circa 
dxem  fttum  facile  qnidem  volvi  >  ac  non  e  lo^ 
co  foo  dimoveri  queat^  Id  genus  trocblet 
plerumque  vifantur  ad  fontes,  e  qoib^s  aqua 
ope  catenat  vafi  demiffb  iliigafx  hauritar« 
Trochlea  ^ioti/r/  oft,  in  cujus  centro  pondus  ap- 
penditur^  &  ip(a  continenter  de  loco  fuo  di« 
tnovccur* 

r  Sehh 


to^  conJkSiu  t^rp^ruwi  MS 

SM.  tr^ibtea  0mnu  vt  vmi  yeStt  t&4  tn  troct 
lca  potifiifn«ili^conrKicrs*ri  dcbct  diameter.  Circuvfe- 
r#fmrf ,  fcu  "figura  orbicularis  fcrccopduci#a4  toUeiidam 
dunraxat  friaioncm,  &  attritioftcm  funium.. .  Et  srocb- 
ha  ^uidcm  fiicti  fpccfcs  ^ft  vesff»  beterodromii,  Hypn-: 
mocblium  {fig.  16*  )  conftituitfir  in  C  centro  figura  or* 
bicuiaris.  Fotuitia  appUcatur  cxtrcmo  urii  B^  pondui 
•Itcri  A.  Eft  vero  JC^  BC  (  ctim  ^C,  &  BC  i\nt  ra- 
iiiejusdcm  cifculi)  ;  quarc  'dtftantia  potenti^  aif  hypo- 
tnochlio  aquatiir  diftantia  .ponder^  ab  eodem,  Tvochlea 
4ttobilis  (fig«I?.)  aHve^lis  bot/iodrcf/my  cujus  cevKro  C 
affgltur  fondiis\  hypoifioMittm  cft  in  csrfcmitate  A\ 
foteutia  in  5.  Jgitur  diftantia  ponder/s  ab  ^hypomocbljo 
tfl  ftmidianteteri  potentia  diameter'^  fivc  diftantia  iUa 
tompofita  fe  babebunt  ut  l  t   %• 

$.  137.  In  trocbkd^  Jtxa  re^ulHiur  potentU 
pDfiMri  fupntanJo  afttslis  i  naiti  tfocfalca  Veais 
e(t  {§.  pr^.  Sciol )  ,  vcl  ccrw  Veaem  imita. 
tn.%  In  vc^ac  pondus,  &  pot^ntia  funt  in  ra- 
t^-.n«  invcrfa  dlftantiarum  (§.  l^SOi  efgo  fi 
G»fl:anii«  funt  acqualei,etia^  potentia  pondc- 
fi  acqualis  elTc  ciebct»  Atqiii  pofita  tfochlea 
fixa  diftantiar  pondcrts,  &  potentia:,  ab  hypo- 
mpchlio  funt  acqaales ( §•  prdc.  SchU  ) ;  ergo. 

CdraU.^  Efgo  troebloa  fixa  ;ie<it4qiMiiii  augctpotcn. 
tiam.  Sed  iion  iirireo  e)usdcm  ufus  continuo  cu  reji- 
Cidndtti  }  praptei:  cnim  commodom,  quod  fublata  friclio» 
nc  creat,  apta  eft  ianQiutarc  dir^fiioncm  potentia?^  quod 
quam  iniigni  emolumento  fiat,  nemo  non  videc.  In 
cxcmplo  iiteqiiuS|qui  juiita  dirct^ioncm  vertiealem  tfa- 
hcrc  ncfcit,  fedduntaxat  horiiontalcm ;  non  crgo  attol» 
let  pondus  opeftmis^  ctii  copulatur;  attoUet  am«m  ^c 
trocbJece,,  vi  cujus  dircdio  verticaUs  abire  potcft.  ii>  bo* 
rizontalem.    IterufH  in  excmplo  fint  bomines,  qui  e  \o* 

*  co 


2ft4  &aion.  Cofut  vS 

co  homiltore  pondus  attollendttm  babeant.  Si  fnne  liia» 
pHei  otentur.  neoeiTum  ertt  curvare  corpus^  qua  'Corpo« 
ris  inflexionrhebefeent  vires,  &,a{ndue  corpus  facig»* 
bitur.  At  fi  fuperne-  trochlea  (ixa  appendctor,  &  fune 
circufnagetur/jnin  iii  iitu  re^o,  ac  natuiali  pondus  tra* 
hent  minore  virium  laffitudine,  ac  proinde  viribus  va^  \ 
lidioribus. 

■ 

^*  1 3.S«  In  trocbks  mobiU  fufficii  Mmidia  p0* 

tentia.  ^  Hic  cnim  diftanria  potcntia^ab  hypo-  " 

mochlio  dupla  cft  diftanti*  pondcrts  (§.  1 3^. 

^cboL)\  tfgo  pondus  duplum  cft  potcntiae : 

^  potcntia  fubdupla  pondcris,  b.  c.  dimidia. 

ScBoi.  Vi  potentia  facilios  trahat ,  poteft  trochlcc 
moblli  adjungi  trochlea  fixa.  Sic  opponunior  crit  po* 
teiatix  diredio.       ^ 

§!.  139.  TrocbJca  compofits^  afitcr  f^fp^ 
ftus  di(5laycftmacbina  conuans  pluribus  troch* 
Jois*  Si  dux  trochlcx  componuntar ,  Jyfpafius 
auditj  fi  trcs^  trijpaftus*^  fi  quatuor,  tnrajpafius 

&c. 

< 

SchoU  1%  In  hac  macfaina  trochle^  alitf  iunt  fx4^ 
alic  moUlcs.  Fixtt  omnes  uni,  ac  cidcm  capfir  |n(eram 
tu>.  Scd  tk  moMes  omms  eadtm  thcca  cttftodiuutur. 
Fofuhs  appenditur  ctnuo  oitinw  trochlcst  mobilis.  iih 
iMf  cap&  .rotnlarura  mobitiam  intertus  «ircum  rotuias 
omnes  dttcitur.  Posifim  nitimi  fanis  cxtremitati  «p* 
plicatur.  • 

.  SchoL  IL  Vt  ae  polytpalH  altitttdo  in  nimium  es« 
creftat,  trochlest  (prsfcrtim  fi  plurcs  &9}  ^^^  %^ 
fed  jtixra  fe  loqanmr. 

•  f.  14P. 


\ 


^i  140.  tft  polyfpafto  ejl  pctentia  ad  ponduf^ 
m  unitas  ad  nunnrum  funium  pondus  trabentiUm 
dempto  co,  cui  immcdiate  applicatut  poten^ 
fia.  Qiiia  cnim  pondus  funcs  fingulos  «- 
^juaHtcrtendicj  totum  pondus  pcr  eos  «qua- 
licer  diftfibuifur}  quare  potcptia  nihil  fuften- 
tapdum  habet  praetcr  ponderis  partcm ,  qiiac 
funi  ultitTio  tribuitur.  Eft  ergo  potentia  ad 
portdus  &c*      ^ 

icboi  t  Sit  ifig.  t|.)  fentfclpaftd  annejctim  ptflt* 
Am  too  librarum^  quod  in  funcs  quinqoe  (  nam  quin- 
que  troehleis  totiderti  refpondcnt  funcs  pofidus  tf •hcn* 
tes  )  cquaUter  dilb:it)uatur  $  funes  iinguli  fuftcntabunt 
lo,  libras*  fiini  autem  qili^te  funes  cqnalitcr  t^nfi 
Ininent  iti  *qtiilibrit)  \  pOf cntia  igitGr  noti  fiifi  pondiW 
qmmo  funt  tributum  fuftentare  dcbctyh^^^  e.  soAfoiani 
,  libras*    Vcrbo  t  habebitur  proportio  s  x :  1 06  =:.  x  t  5« 

loot 
Ptoinde   5*  =<    teoj  St  *  ^  - —  ^  ^o* 

ScboL  tt  §i  pktcs  poly{pa(ii  cohjttfigeflttft  *  trf 
eihibet  %•  19.,  perinde  fuerit^  it{\  potcntia  im* 
polyfpafti  applicaftetttr  ccn  potodos  fcctifidflb  polyfptfftOi, 
Qnantcf  virium  coftJpendiO  plttrcs  polyfpSfti  conjuftgati- 
tur,  patebif  In  excfhploi  ,  Sini  du*  Pchtalpafti ,  qni- 
fufti  admifliCula  lcVandjt  fiftt  looo;  nbf«t.  Si  tinita 
^ehtafpaftus  adhtbcatot^  trah^iir  pohdus  fhtiibuS  quin- 
I     quc;  qtltfre  habcbhtir  prbpbrtiot  *  :  1006  &J  I  :  5* 

loodf 
^ct  fubinde  %x  =?  lOOd,  &  *  :i5    ^'ir-.- ^•>-«'  S  ftobi 

5 
h*e  eft  pdtehtid  prltn*  foH  f oiyfpafto  coh^chichs,  'fi 

potemisr,  &  po^dus  jtqfliHbrare  dcbcarit,     Scd  ipfa  haec 

petcntia  polyiptfftcr  altcri  ippbcetisl'  inftir  ponderiS;ha- 


* . 


I 


bebitQr  ittttim  proporclo  i  X  ttoo:^  t'il  ^rgo  sc  tS 

«00 

•— — «  =j  46.     QvuLtc  debebit  {)Otemhi|  libns  40«  Cu{!d* 

liere  taleiis,  xooo.  libras  in  «qoilibrliftte'  rotftitierq« 
Ergo  fi  pottiuia  ^quabituir  libris  41.  «ttoU^t  poadttd 
ai    1000« 

^.  li^r.  Axii  in  pitiitochi^  eft  fOU  c\ftX 
axemi^m  affigietir^  volubilts  (fic  Vero  affi* 
genda  eft^  ut  rota,  (ive  pcHtrochi$  gyfantei  etU 
atn  axiS|  queni  Veteres  cjrlindrttm  vocabant^ 
gyret^)«  Suffictt  immo  circalum  concepii&l^ 
qui  defcribitur^  dum  imerea  cylinder  ppe  te^ 
monisi  aut  fiytd^rum  (quas  Latinira^/  trmts^ 
vcrfii  dicune )  circum  axem  fuum  revolvitur« 

Schoh  t  I^tlpleig  tft  a:itti  itl  pefltrocbtol  fi  dkis  ^ 
fcu  eyiinder  boriSonralis  eft  (figi  io<  )  JTfrctt/a  didttir  ^ 
fi  verticalis>  Aj^a/4  (  %4  ^  1 O*  ^C9$latH  dicunt  ponderu 
bus  in  altum  levindia  opportoiiiorem  e(fe,  Brgatdm  ho* 
rizomaliteri  aut  per  acclivitatett)  proroovatidis.  ^ 

ScM*  tt  In  hatf  cnachiiia  flpplicatiir  potetitia  circitm- 
ferentic  rotaf  (  qtiani  alii  tymfauum  vocint )  $  Vel  eKtie* 
mitaii  fcytalarum^  aut  tcttiorits.  F^uiiu  e  fuHepandiTlttttl 
axi«  Ifyponioebliou  eft  iii  Caniro  axis,  ka  cylindrt^ 
Igitur  axis  in  pericrocbio  Vecli^  eft  hoinodroinus  itni 
gmeris4  Si  rota  circutnvolvetur  (emet^  etiam  ajcis  ro* 
tm  ifnmobiiiter  affixus  eodem  tempore  gyrabit  lemelj 
&  funis  cylindro  obvolvetur ;  quare  {icut  rotn^  &  axia 
de(cribunt  peripherias  {iiniks,  Itc  &  arctis.  Saitt  ve« 
ro  arcus  illi  (patia  perCur^  eodcm  tempore  a  poteiitia^ 
4tc  pondere;  dcfignabiint  itaqoe  celerhates^  erttqaa 
ceUrim  potemia  ad  ctkritatm  pcndetis  ^  m  arcus  Ji" 
Jcriptus.  4  rosa  ad  arcun$  defcrijtutn  ab  axc*      Sed  ar<' 

cua 


CQS  (imiles  fbnc  t^im  proportiontles;  etiftm  ergo  cele* 
jrita^  potentis^  ad  celeritfltem  ponderit,  ut  radias  rotc 
fld  radiutA  axis.      lEx   ^no  itqtiens  thcorema  dcdu- 

ciruri 

§.  142.  Sl  poimtU  9pe  §9cis  in  fmtr$m 
ibio  pondus  Jufiintan  dthn  ^  fit  poteniia  ad  Pon^ 
dus^  ut  rsdius  ssxis  ad  rskijum  rotst.  Ut  e« 
tiim  machina  hcc  veAUi  in  qua  potentia  1  & 
pondus  fubt  in  ratione  inverfa  diiftaneiaruni 
(  §•  1 3  5  • }  •  Diftantia  pondirii  ab  by pomocblio 
hic  quidem  eft  radius  axis.  Diftanti^pountla  ra- 
dius  rotae  [ScboL  prac^^\  debet  ergo  potentia 
efTe  ad  pondus^  ut  radius  axis  ad  radium  rotsr^ 

JScUl  L  Radio  axis  addendas  cft  radias  fonis ,  4 
quo  pondus  peadcti  camprimis  fi  funis  craflittftulus 
<rit. 

SehoL  IL  Raditis  axts  dteatnr  yt^  radias  rotse  R» 
Erit :  p  t  P  s  ^  ;  J{.    Proinde  PA  s  pR.    Queri» 

tur  jam  potcntia  datif  trihus  C€tork  %  crir  f  r:  —  • 

^R 
IL  Invcnicndum  fitpotidasi  fict  ?  s  — *^«    IIL  Si 

i  ^ 

>  pR 

radins  axis  dtfidcrcturi  crit  j1  a  •*-—  «     Si  IV.  ri* 

p 

■a 

P^ 

dius  rotsr:  habcbitnr  R  a  --— •     Hec  numcris  ap« 

'  plicanda* 

SdoU  IIL  Qoantumvts  rxis  m  peritrocliio  miro 
txaogcac  vircs  potcntiei  firpc  tamcn  snachiiia  hec  in* 

Vn  *         foffi 


/ 


n9  S$Qi^  tl  Opm  V. 

iiifitcien$  cftttiilenundo,  «ut  iev«ndo  pr2gr4ndf<cnu 
^ani  pdnderi ,  quod  viin  potentix  naturalis  mulcam 
cycadir.  Oalio  a  potenrja  ;=:  ^o  lQAincnd6in  eHe  pon- 
dus  s3  3000  libris.  Radiuin  rumain  tz,  i  pedi,  ut 
pondoi   tautam  ferre  rMeat.     Quoniam  p  :  P  :=:   A  i 

PA  3000 

X,  &lt  r^   ■   ;  ■ ,  radlos  rotx  «quaret- —  =::  66  pc* 

det  ^  iafiixtt  oporreret    abiiorinis    iiiaghicudinis  rorant 

confirui,  quod  in  praxi  fieri  vix  poteft,     Hutc  inconT'^ 

modo  QC  mcderenrur  Phyfiei , '  medelam  qQxfierunr  & 

invenerum  I.  In  poiy(paitis  una,  auf  piuribus  /  quas 

axi  in  peritrochio  frequenter  adjungum.     Ih  h\  mul- 

tiplication»  rotarum  cum  axibus^       Atque  ut  rota  alia 

aliam  cireuidlgere  poflit,  in  extiiTia  peripheria  dencibus 

h.  e.  intcfrtallis  ah^mis  dehifcentibus,  ac  protiiihehtibifs 

cas  inftruxerunc  eo  conniio,  ut  denrcj  rota^  tmius  inrr^ 

^pta  dentium  alrcrius  infeti,  ficquc  rorrf  rdtam  circum- 

flgerc  poiTir.       Rotac  aurcm  tfnin^s  fexcipid  earfi ,  cifi 

porenfia  applicatur  ),  oinnesque  axcs  (  dcnipro  illo,  cdi 

fonis   pon4us   trabens    alligatur)  dcnres  fuos  habenr« 

Hoe  aggregarum  axiuin  in.  peritrochlo  revera  eft  cqn- 

gtrics  pluriiim  ve£liliim  ;  quare  machina  iflhxc  cundcm 

canonem  .feqoetur  y  quem  vtAis  cooipefitusi     Nemp»»* 

fi  flures  pnt  axes  in  peritt-ocbio^  e/l  p  :  P  ficup  fa^iitji 

ex-radiif  axium  ad  faRnm  ex  fadiis  rotarum,       Qua^ 

re    dirris   cxteris  fapile  jdererminabirur    fivt  posjsnciff, 

(ive  pondus,  (ive  produ^lum  ex  radiis  rotaf uni,  &u  de« 

nique  ex  radiis  axiuifi.      Lex  ifta  tiniverialis  eii,  fcque 

.  •Kpbrrigir  non  m6.do  ad  omnia  g/oJfoeomOy  (euvad  eoHi- 

politos  axes  in  pcritrochio  ,    (ed   cciain   ad    madinar/i 

Gruis^  qudb  a  Glodocoino  hon  differt,  niG  qubcl  trocb^  ^ 

.  leas  iibl  habeat  ^djxintUs^fixaiu  in  rollri  cxtcoipitate^'& 

mobilem  idfcrne  locatain,  a  qua  pondus  dcpeudct. 

^.  149.   Planum   inclifjatum   toco ,  quAd 
cum  plano  h  omomaU  fach  angfilum  acu^4ni# 


j 


Stt  ^lqm  reAanguliim  ABC  (  Rg.  a$.  ).  Bm 
iis  iBC  exhiber  plmium  horizontalc.  i^C  hypp* 
fhenufa  defignaf  plani  jnclinati  hngitudimm. 
'4B  aleitudo  ^li  refert  flani  inclinMi  dltituS^ 
ptm, 

§,  144.  Si  op€  plani  inelinAti  AC  p^intis 

'direiiiofu  plMto  paraiipla  fufiintH  pondus^  trit  p0^ 
Untia  ad  p^ndus ,  ut  altitudo  plani  AB  ad  tjut 
hngitifdiktm  AC^  Dum  pondus  ex  C  elev^- 
tur  tn  f ,  aflurgit  ad  altitudinem  JfiC  Cconci- 
pitiir  ^nirn  totuo)  pon4us  in  centro  tanquain 
fn  punfltQ  colleftum),  Intere^  vero  potcq- 
tia  eodem  tcmpore  decurrit  fpatium -EC  dirp- 
'iftione  plano  par^Ilela.  Hic  vero  habentgr 
•/\Ia  fimilia  ACBy  &  JfC/C  (nam  angulus  K  ^ 
^ngulo  Bi  cumque  EC  parall((la  fit  ad  AC^ 
fjfiam  angulus  MCK::::  ACB^  ergo  tertius  jB 
r:  A  tertio)^  conferendo  latera  homologa 
"bafbetur  proportio;  EK  x  EC  zi  AB  X  AC^ 
Quare  ficut  per  EK  defignatur  celeritas  pon- 
^eris,  &  per  £C  ccleritas  potcnti*  (quia  fi  T 
tz  r,  eft  C  :  ^  z:;  S  i  s)  \\q  pafiter  ratio  ce? 
leritarum  defign;|ri  porerit  per  AB^  &  AC. 
E{laium)^nis  duarum  virium  mutuo  in  fo 
deentiuiT)  :=  vi  abfoluta;  multiplicatas  per  rpa<^ 
tium,  zi^t  celeritatem  (  §.  104.  )•  Nifus  po- 
tenti«  vocetur  pi  ponderis  P;  erunt  poten- 
tia,  &  pondus  in  «quilibrio,  fi  pAC  :=:  PAB^ 
quc  h&ti,  =:,  lia  (blvendo  tn  proportionem  ob» 
tjn^bitur^  :  P  =5    4B  i  ^Cj  five  potmia  efi 

P  J  *       !     Coroll 


Sjo  SfBhlf.  Csfut  r« 

Cort4t.  I.  Si  /iC  famattir  profim  rm,  fire  pro 
ra4i§.  cirmlty  <fA  e  ceotro  C  defcriberecur  intenralia 
^C,  erit/^^finusangultindinationisyfCBi  quare  coia 
p  z  ?  di  AB  ;  AQ^  crit  potetnia  ad  fondm  Jk»t  (mm 

anguiti  ifieUnatioms  ad  radium, 

C$roU.  It  Ex  intea  dtdla  conficitor,  qnDd  mn* 
Ireiite  ead^fit  plani  incliiHlti  longitu^iite  pondi»  idem 
co  minori  potcnria  ibftentari  poifit,  qoo  ininor  habebi« 
tur  plani  altttudo ;  &  rurfiini :  quod  manence  eadem 
plaoi  altitudinc  potentia  eadcm  boc  tnajua  poiidiis  (il« 
fltntarc  debcati  quo^ajor  fucrit  plani  longitudo, 

§.  14^  Si  dinStia  poUfaia  funit  ha/i  p4^ 
raUcla ,  0rit  potentia  ad  pondus  ui  ahituda  pUni 
dd  baffm^  Supponatur  potencia  diredione  ba* 
ii  parallela  agens  ope  plani  inclinau  pondus 
trudere  horizontaliter.  Dum  ica  procrufurn 
pondus  eleTabitur  fpatio  £K^  potentia  decur* 
t€t  lineam  KC;  ut  igitur  potentia  fit  par  fa* 
ftentando  ponderi,  oporcet  potetitiam  ad  pon»^ 
dus  efle  in  ratione  inver(a  harum  linearum; 
five  efle  debet  p  :  P  e;  EK  :  KC  Porro  j 
cum  EK  :  KC:s^  AB  :  i?C(§,/T4fC,)eritetiam 
p  i  P:::  AB  :  BC.  Atqui  ^ijB eft altitndo  pla* 
Yiii  BC  bafis  j  ergo« 

^.  14^.  Ponduf ,  quod  faper  plano  in# 
clinato  movetur,  driplicem  hjrbet  gravitatcrn; 
sbfolutam^ic  rcfpfflivam^Ctu  ^omparativamn  Vim 
gravitacis  aifolutam  voco,  qua  urgente  corpas 
delabererur  fecnndum  diredionem  naturalctn 
gravitatis,  id  odi  pcrpcndicukrittT  ad  hori«on- 
tem  ^  fi  nullum  adellet  planum  inclinamm« 


C.      . 


Gravitatm  n/hffiivam  dica^  qua  corpus  htC|  8c 

nunc  defcendit  fecundinn  lineam  longltiidini 
pUni  paraHelam» 

ScbpL  Dum  corpm  pir  plamtn  $ncltna$tm  defitfh 
4hy  amittip  partem  gravitoiis  abfiim^;  corpus  enini 
^efcenclens  planam  preinir»  qoit  frcfh  pfr  «qii«ltfli 
plani  reaftioneni  4^firtiitur,  Oritur  vero  prfflSo  ilkf 
m  gmriutt  ^orparis  ab(bii|Ca ;  rrgo  d^fliruitQr  altqQid 
gravitatis  abibluts ,  protnde  nfnirtinir,  Atqpe  JalUtm 
4Ua  tamtp  efl  maJQr^  qtf»  acntiar  fmrit  augifiuf  i im/xm- 
tiofii$\  hani  fi  planum  verticale  foret;  niliil  grancatif 
ilbrolur?  tmitterenirt  4^iaberctarqae  corpiis  omiii  (ua 
gravitate;  fi  iioriifottiale  ftatuatnr»  eildetur  omnis  ndio» 
6^  yn  gravit#ti$  9bibiu?t(  corposqne  plano  ^ori^omaH 
ineumbeiif  omn^m  grtvitAtem  Auim  pmitret ;  er^o  quo 
^ianum  magi»  ici^^lipt  «4  fitiin)  ieri$toH$alem^  hoc  pius 
graviiflis  mbhit*  •mictcr;  quo   magis  ad  ficum  «n^af- 

£alim ,  )»^  maflirw  pMWt^  ftrm»irM  j«d(»tiii  i  ifm^ 
4fi4e> 

$.  t47t  ^  difi^nfi  wparii  pcr  pUnum  in-^ 
dinatmn  ij^  Pif  graviMiif  fomp^rativa  ad  abfitu* 
Um  9  itf  pUni  imHnati  akituda  ad  fjus  Ungitudl-^ 
fum^  Sif  plaMim  incHnatym  JfiC{fij^,  93). 
Exhibeii  i^f  rim  gravitacis  «broiqcanii  ^uss 
fnbin^e  «n  bints  ^lias  reftlyatur  i><7,  &  DF 
(!•  ^»)»  EXpHmot  P£  perpendicuiaris  ^ 
4C  partom  pif  abftlut^^  qq«  per  gravit^rem  clj. 
fa  futt;  0f  Tcro  »9QaIi« ,  &  par^llela  GS^Cr 
^nabit  vim  pamparafivam  ^  oua  corpus  (elif^ 
jamp^irto  graVitatis  abfotuta?}  per  plani  incti- 
nati  dire<ftionem  defceAdcro  nicitur,  Habf^ 
Intof.  auiem  fimilitudo  trianguionKn  reAan- 
gulojrom  JBG9  6i  DEGf      liinc  «oUatts  inYtr 

P  4  •  cf  m 


*/ 


^3^  S^ioll,  esputVf 

C^m  homologis  Uteribus.entG^J?  :  DiE^  AB j 
4Cf     Camc|»e  GE  :=:  DF,  erit  vis  corop^rati. 
•  va  ad  abfolutam^  uc  pUni  iqclin^iu  aUitudQ  44 
Jongitudinem, 

> 

Sehol.  Triaiigula  ^BC\  &  DEG  (tmiHa  efle  pate| 
fX  co,  quod  Alnw  ^BC  fimilc  fit  ^lo  ^WC,ut  facile 
^cinonftrarur-,  -  Eft  porro  ^  EHC  fimilc  ^  D£Q, 
nani  anguli  ad  vcrtictm  £  oprpofiti  fiint  squalca ;  an* 
galiad  G,  &  // redi ;  q[aarc  angulos  GD£  eqoata)? 
angolo:  JfC//.  Ergq  &  Al«m  '^SC  fimiic  eft  AIq 
DEG.  '  •     ^ 

CoroV.  Itecum  vis  alfilutq  cf^ac]  comp^ratham^xtH 
fiim  totm  fiyc  rf<^/^  ad  fifiuiii  i?/ig»/i  it^lifiqtiquif^ 

>^.  148*  fiiVimi  ^Amh  far/i^i  per,pknum  itkt 
$UfMum  dtfictttUty  $fi  vif .  cM$pmrg$ivM  #^  vittt^ 
^  pUmttn  dir$St  prmitur^  ta  4hi$t^  fUm  ^ 
^ut  bafim.  Semper  enitn  (y^.  M^t )  tnangiiin 
ABC^  &  D^Q  (nanebunt  firaili^  Qiiar^  ito^ 
run?  habfcbitur  prppQrtio;  ^£  ;  DCs  45  t 
^C  .  Atqqij  ?rgo, 

Grpff.  L  Ex  cadcm  fim  ilitndtnc  triangDltntro  JBC^ 
ft  DEG  manifeftc  lequitur:  vim  gravitati%  ab(bltttaii| 
effe  ad  viip,  qua  planum  prcmjtur,  utplani  inclipati  loiv 

iitudp  ^d  ejus  bafim;  nam.  dcpuq  or^ctn^!  pr<4>orua^ 
^)£  :  DGz=i  ^C  :  BC.\        ^ 

CoroV,  IL  Nemo  non  vid^t,  qucmadmo^^n'  i^^ 
•  vi  gravitatis  ahfifttta  inveftigari  ppfilt  fiyi  gravitas  rt^ 
ffectiva,  feu  vit  premem;  &  yiciflim.  HiEC,  <&  id  gc- 
nusalia  vclut  fpontc  ifiia  fluunt  e  proximis  quinque  ^» 
ncquc  a!ia  rc  iithuc  ppu^  cft ,  qiiam  quarto  tcrmino 
Geomctr*  proportion»li.  JBcd  &  illud  confeqaitur.x 
^4  gravi(at^,(ovtfarufiva/^cik  dittrminaxi  ^.^^''?'^% 


vr, 


quct  pmdiis  fuflineat^  vd  am.Uqi'  S(  ^ntni  poudus  (u. 
ftcntaiidiiin  efl:,  re<)uiritiir  potentiq  far  gravitati  reffie* 
/?7W,  (jua  fola  cofpns  dcfccn4it  pcP  pJniV^linclinptuni. 
S\  atroll^nduni ,  ma)or.  Pono  phnum  liKlinatiiin 
yfBC  C  fig.  23.),  cnjns  altitudo  y^5  =:  9.  ped. ,  lon- 
girudo  ^iQ  ^  %-i  pondns  fuftincnduin  aqt  rnovcndun^, 
ycl  potius  gravitai  aififuta  =s  40Q.  Erit  cjusdcm  pon- 
flcvis  gmvhns  ($j/}parativq  zx  l5o\  nara  x  :  400  cs 
*•         '  1200 

J  «  8  ( §f  146.  )i  crgQ 8  X qfJ  I30e i  &  a:  ss    '  .  .■  .  -: 

8 
«    Ho.       Potcft  vcro  potcntia  fubftitpi  pondus  (§. 
130.  CorolU)\  ergo  (i  ponduslcx  (roc|il«|i|Ldcpencl$i:vi 
p:    15O1  fultenrabuptur  -joo.  librac. 

^.  149.  $\  planum  inclinatum  in  fuper» 
ficiecylindri  in  orben^  cirgumducirur,  oritqr 
focble^.  Hinc  ^othka  dicitur  cylinder  fulcii} 
iive  heiicibus  incifus,  Si  helices  in  isxtim^ 
cylindri  (upcrficie  circmndu^jp  funti  habetur 
mUcA  filid4\  (i  cylinder  ^4vus  b^bet  heiices 
10  fuperficie  (ua  interna  incitss^  vocatur  mln 
h$  tav0^    Fi4c  fi^,  24, 

Sgh^L  f,  Cochfc^  r^  yera  eft  plaputn  iiicHtiatum* 
Hujns  altittida  dcfumitur  a  diftantia  duarum  proxima- 
rum  hclicum ;  iajit  a  cylindri  pcripherii|.  Dum  vis 
^cu  poc^ntfa  mQVctur  peir  periphcrjam  cochlcap,  pondiis 
inrcrc^  dcprirnitqr  pcr  diftantiam  uniiis  hclicis  ab  alte- 
ra ;  quarp  efi  fpqtium  a  potcntia  decurfum  tid  Jpatiwn 
^  pondcre  confcftum ,  ^t  peripb^ria  cochiea  ad  di/lafi' 
fiam  helicum^  fivc  ^t  baQs  piafti  inclii^^ti  ad  cjvu  alt}- 
mdixicin.  A- 

Schoh  It  Ufus  cochlcae  qnotidianqs  cft ,  maxime 
ih  ;oin|)riffi^ndis  qorporibMs»    S^d  podll^  roUdae  jan- 


.  .!/ 


2i4  S€m9  /t:  c^  r. 

gi  debcr  cochlea  caya ,  cajos  bclicct  ira  {iict&  (laty  uf 
fulcos  cocblcs  fbliddP  exadc  rccipiant  \  hinc  cas  in  cjr* 
Isndro  urroque  ^jnr  difimw^  ^  f^ralUias  cfTc  opor* 
rerf 

$•  150«  ITir  p^  miks  foimiis  pndm  ir« 
guilihrftur^  ddf^  pounUs  fvUmlr^  innmdiMic  t^ 
plicgta  ep  adponduitut  dijf^ntid  dusrum  btUcnm 
sd  cylindri  pcrfphcrism\  nam  fi  fnofnentuin  po» 
tentix  dtc^tw  pc^  &  momentum  pondtris  PCt 
efle  dcbet  pc  =s  PC;  proinde  p  :  Pzz  C  i  4 
($-133')*  ^^^  Ctlive  celerit4S  ponderis  ed 
dtftantia  doarum  belicum ;  irerumcjue  r,  five 
^leriras  potentiie  eftperipberiii  cylmdri  (  hxc 
cnim^nt  fpatia  a  potenna»  &  pondere  con^ 
^a  $,  ^^^  5(M  /• ;  fc  fpatja  eodem  temporf 
confe^a  funt  ut  celeritaces  §•  ^i»  &M  Z^/») ; 
crgo,  N 

CproV.  Qu^  ^profinfii^S  fi^rinc  hdieis^  koc  mf" 
nor  requirimr  fotemiai  miiiori  eniai  ?icinitari  refpeiu 
(ier  minor  didanria  helicnm ;  ergo  cain  potcpii«  fii|t 

ut  diftantie  belicuip  proitimarmn  dcc»\ 

Schol  h  DixiHiperinst  fotefusa  tpweeJfate  offU^ 
eata  cylindro  efi  a4  fondm  iSfc^  Scd  in  praxi  non  ini* 
mediare  applicatur  potciuia  cjrlindro;  cochlea  plcrum» 
quc  ope  tcmonis  conv^rtitur ,  aui  cylindro  affiKUi  ef> 
format  axetn  in  feritrocHo\  ncque  pr^rcr  efficaciri- 
tcm  cochlca:  multum  ^ugerur  vis  porentis,  cum»  qot 
prius  tvaifotentia  rcUte  ai  cocbkam^  delnceps  ut  fot^ 
dus  ipeflctur  comparatp  ad  4xem  tn  peritrocbiOf 

SpboU  Jl  D^  (coehlea  htfiaifa ,  ftu  fcrfetua  (fy, 
95.}  nihU  mj^morabo,  nifi  quod  non  cpchlc^alturiiiv 
ftratur^  fed  duntaxat  rotam  radiafam,  cu/u^  i^m^s  ju^' 

t»    " 


vt. 


ta  obU^ttit«tem  'helitnm  ebchle*  inddi  debcnt,  pcrpe- 

tiio  circiUTiagit;  tflqnc  tnt)ttrt  illjus  tardiflimns,  quia 

dum  cocKlct  eircumvolvitur  remel,  rota  non  promovc- 

(ur,  nifi  dentis  unius  intcrvtllo,     Cochleam  infiniram 

dentibus  son  ampUus  tribui  intljge/e  adnotavu  /Fo^ 
fius, 

r 

S.  151.  Cunmt  eftdupIeK  plantim  inelU 

fiatam  in  eandem  aciem  deiinens  {fig.  26. )  • 

.    Altitudinem  cunei  defigntt  linei  CDi  ba(im 

ScMr  Alit  euneum  dicunt  prismt ,  cnjus   btlcf 

^  A^^  Ififi^^f^»  ^^^  dcfiniuntalita:,       Multoa  imer  lU 

cfl ;  ad  vedem,  an  ad  nlanum  incHnatum  revoeari  de» 

beat  cuneus.    Ego  iftis  non  immortbor*    Quod  ce^ 

tum  habcpf  do.  '  j 

'  ^.  152.  Vt  pctentis  opc  4unH  fufimtH  ppn* 
dut^  tjfc  deht  Potemia  ad  f^ndut^  ut  It^itudQ  ba* 
f$  in  cunco  ad  ejut  dltitudinm*  .Nempe:  dum 
caneus  infigitur  trunco  ad  altirudtnem  GD^ 
re^lh  rruncus  fpatio  MF^  quar  fpatia  codem 
tempore  confeAa  iunt  ut  celeritates  potenti^» 
&  ponderis,b«e,cunei,  &  truncii  ergourpo* 
tentia  ope  cdnei  fuftentet  pondus,  eUe  debec 
,  j>6Dx:  PEF.  Iterum  quia  C^lumEFD  fimile  A^o 
JBD  (quod  cx  parallelis  AB^  &  £f  contitiuo 
deducitur>  erit  etiam  pCD  sz  P4B;  proinde 
9  t  Pzi  AB  t  CD,  Sed  AM  eil  bafi^  cunei; 
CZ>  atHtudo;  ergd, 

OrolL  Ergo  qm  aeutior  fiserit  eunem  ftti  eadem 
hngitudinfy  tmto  erit  efficacior ;  nam  quo  acutJor,  hoc 
|Di&or  iliius  bafiii     IL  Quq  mimr  fytrit  imntdo  eu» 

nei, 


..^ 


/ 


«3^  SeSicfll.  €^  Vh 

nti,  boc\  mimr  requiretur  pctettti^;  eft  cnifii  f  ;  P  ut  ' 

bails  Q^nei  ad  c)u$.aititudinepi  |  crgOf 

Scboh  t .  ^d  oaneum  rcfernntar  cultri,  gU<Ji',  <5cnt 
f  es,  I  oftraj  clavi ,  unguc«  animaiium  ,  ac  praccipue  ton» 
ibrum  novaeuiiip  fic  cdidtr,  qux  quit  iutrorfiliit  cai^oc  (unt^ 
facjfliine  qmni^  pcnetr^n. 

Scbai.  II.  Ifta  euuei  tlieorit  in  jpraxi  hqa  (empep 
of3tinct,e.  c.  in  liguis  cunci  opclfndctidis.  Lignorufii 
fbrqp  aivQrOmpd^spohaerciTt;  iion  ccdnm  fingal*  «quM 
biliter,  ac  per  {|>atia  squalia.  £(l  hic  pljprumque  |>0- 
t<Hpa  cwiei  ad  vi^*  rejtfie^iwn  ligniy  u$  dimidia  bafy 
ad  l$tu&  cmei,  ut  egrcgie  dcmonftratum  babet  F,'  Ma^ 
ko.  Quod  de'  cuneo,,idem  de  aliis  mgchiDis  di^lqtn 
efto,  m  qutbus  Czpp  ^riHta,  funium  rigidiras,  aut  grat 
vitas  6tc.  motum  rcgularein  impedipnt-  Tii^oria  nch 
(Ifa  pr^iciiidit  ab  ejustnodi  tmp^dimcntis. 

Caput  VL 

De  motii  graviuni. 

§.  153-  Oravia  dicimuj,  quapcunque  fihi 
reVx&a  verfws  centrum  telluris,  auc  interiora 
terr«  feruntur*  Quare  gravitas  eft  vi$,  qua 
corpora  verfus  centrum  terr^  yrgentttr,  aut 
prope  illiid. 

§.  154.  timA  iorizontahs  diciiur,  cujiii 
fingul^  punda  a  centro  telluris  drqualiter  di- 
ftanc  Hinc  vcr^  linea  horizont^lrt  ^ft  arci^s 
circuH  e  centro  terr«  defcriptus.  Ac  eninv; 
ii  circull  njajores  jrup.t  j  chofd^  parvartim  ari 

' '  '         cuum 


pe  cdHfiiSiu  totp^tum  Sj^ 

igaittli  fdfe  Qiini  arcubus  eotnciddnt»  ^el  cort6 
lenGbiHter  ab  iis  non  difcrepanc;  quare  po^^- 
teric  qosvis  reBA^  ^uk  veram  horizontahtn  iH 
pundo  ungit^  haberi  pro  horizomalii  Ha:c  re^ 
^a  dicitur  hofmnulis  appdrifnti 

SM,  Nihil  cDcft  dciiVihioni  linc«  hori?6fitaliiy 
quod  figuiatri  teliuris  ^baroidicam  eilc  fuBlnde  anere* 
hius^y  nam  proximc  «Ccedit  ad  Cph^tktim^  &  ad  Jenfum 
(ph^rica  cft. 

-  ^     $•    l^^J-  ^'  eehirum  ^^UiiihtH^  quod  fimill 

(  fahem  duiti  vites  a  gravitate  proVeniunt ) 

eft  centrum  gyaviUtis  ^   lUud  puniftdm  dicituf  , 

cujusmotu  impedico  omnis  rnafla  immota  ma-* 

tiet  (  §>  i  3  !• )  ijuid^uiJ  ienttum  gtavnatis  Ju/linu 

bit,  tGtum  iorpotis  pohdus  fuflinebit.     Inde  vero 

Uta  c&rporis  gravitas  cokjtdetari  poterit ,  tanquam 

Ji  in  punSlo  unico,  videlUei  teHtrb  gtavltatiStoUt^ 

(id  foret.       Qdafd  liftea  fe<3:a,  ^uatn  Centrurti 

gfavhads  defcribit,  pfo  fpatio  a  cofpore  gfa- 

ti  defcripto  hdibeticla  efi^A 

ScM.  Ehttti  <*orpt»ra  hbcrc  m  tcM^tM  ^clafeuntaf , 
Jn  lii>my  rcftis  a4   fupcrficicm  terrvptrpvndtcttiarihu 
delabuiirur.     I^crpehdiCQiaris  cjusthodi  dicitur  liuea  ii* 
teCtionis  gravium  \  proindc  &  eefitn  gravitatisi 

§,  1^4.  Siy  dum  twfnf  Ji^eneHturi  lima 
fiifpenjionis  ^   iS  lineM   direStionis   centri  gravitafit 

funt  in  cadefh  reBa ,  eorpus  grave  fion  tnovctut  ^ 
Jed  qiiufcit:    Pbfeft  enlni  pUndiufh  fiirpenfib- 

liis  coniadei^ari  Veliit  potentia  quxciam  rbidetrf 
'  appticatfi^  &  v)m  graviucis  elid^ns;  ergo  ^u 


238  SiShlL  CdputVh 

ttStxo  hujus  potencia;,  &  diredio  pofideris  lea 
ceticri  gravitacis  debent  fibi  e  diamecro  oppo« 
ni|  h.  e.  jacere  debenc  ineadem  redta^  qoare 
viciifim  fi  pundtum  (urpenUunis,  &  centrum 
graviratis.  fint  in  eadem  reda  %  fibique  e  dia« 
fnetro  opponemur,  vis  gravit^cis  elidetur;  ac 
proinde  grave  quiefcct.  II.  Ccncro  gravi« 
tatis  corpus  dividitur  in  parces  da.)s  arque  gra- 
ves;  quare  pars  una  tantum  urgenir  deorfum 
e  latere  uno,  quantum  altera  cx  alccro»  Non 
igitur  fubeft  ratio^  cur  pafs  una  artollatur  po» 
lius,  quam  altera.  5i  neutra  actollicur,  gravo 
quiefcit;  ergo. 

J.  1 57.  St  gTAVt  quoJcun^M  Jre  in/ljldi  pJa^ 
no  koriZQntalif  ut  Unca  dirt8ionu  ctntri  gravitAtii 
iadst  intra  bafim  plano  incumbtntm^  corput  a  Up* 
Ju  mmune  mt\  nam  fi  iinmune  non  fit^  cadet 
juxu  lineam  diredjonis;  atqui  juxta  hanc  ca* 
derenequit»  cum  juxta  illam  infiftat  planoi 
cujus  refifientia  fuperari  non  poceft.  11.  Si 
linea  direAionis  cadit  incra  baum^  fuAentatur 
centrum  gravitatis ;  proinde  &  totum  corpo* 
ris  pondui  ralftentatur  j  atque  adeo  grave  non 
ruet* 

Schol  Hinc  ritio  datur,  ctir  homines  caroi  proxi* 
Hit  bracbtanii  vcl  pfdtni  attcrtHn  in  partcm  oppofitam 
cxtendanti  nempc;  ac  momento  in  parte  lapCiii  con* 
traria  ando  direitio  cbmri  gravicatii  intra  bafim  cadat 
fimilitcr  cur  obcfi^  atic  onus  quodpiam  antc  (c  defe* 
rcntcf  retrorfom  corpus  iiifle£lint;  gibbofi  eontra,  & 
itt  dor(b  enuAi  antrorfum  flc£iantur'|  cur  (enecio,  qui 
fob  gravi  cmibram  ponderc  curvatus  incedic,  baculi  au« 

*  xi« 


N 


jtittO  tieitur;  «ur  turtcs  j  aiit  iiiUri  tiort  tnodic*  ^cclk 
'  Jiati  ttoft  taiticrt  coitUatit;  cut  iliqui   in  t.nfis  fimibus 
ftcile  inccdinf;  Cur  pucrum  pcdl  uni  i»T(i(^cmcn»  j   ac 
&ltilttlltctn  iniigniter  cautiim  e^t  i»p6tmty  i»c  cadat. 

$.  t^%.  Si  Unu  dittdmii  adat  cxtra  ba- 
Jlmp  tuit  gfAvc  \t\  eAtti  partem ,  in  qiwm  de- 
clinat  iinea^  cum  enim  nihil  impedit,quo  mi- 
tius  juxta  eam  eorpiis  guve  moveatuf;  ruet 
Sgitur  eousquej  dum  mucatum  centrum  gravi- 
titis  cadat  intra  bafmn 

Svbot.  Vi'3tt  de  etntro  gravitatis  eorpofum  fingnh- 

iim  fkwptorUvt^  Jani  qua  racione  ccntruni  gravitatl^ 
liuoruin»  aut  plurium  corporuih  inveftigctur,  pauris 
doccbo*  I.  St  duo  babebuntur  corpora,  fecmtr  rdla^ 
quae.  cttxttiL  Jmguhrum  corporum  conjungiti  in  ratiom 
tcciproea  corporUnt.  PunAum  intcrfcAionis  dabtt  com- 
ttiuhc  ccntrum  gravttdtts»  Vcritas  harc  defnOnfiratur 
Jt  tbeoHa  vettk.  IL  Si  plun  fuerint  corpora^  ducator 
j^riibum  rcda  conjtttigetia  cctifra  duorum  quorumvis 
corporumi  eorumx|u^  eeutrum  jgraititaiif  comtfmni  tio- 
tcc  111*4  Huic  tioviinme  ittvemo  )ungatur  ccntrum  tcrtii 
alicujtui  corporia  pcr  retilam»  qu^  itarum  in  rationerc* 
eiproca  fummdK  malTarum  priorum  fecanda  eft^  &  (ic 
it  cacttris  ^  puiidum  ultimde  iittcrCtdiotiis  crit  eom- 
mune  tliud  ccntrum  gravitatis  quotcunque  corporum. 
tnfera  1  ti  eorporum  quofcuttqiK  eentra  gravitatis  ja* 
ccant  in  «adcm  rtda«  Itaiiptr  commcine  ctntroi»  dTe 
dtbtt  in  attqiio  ^uidim  rtQte  fisftClo. 

$*  159.  Cfrpara  travia  ab  aU9  delahntis^ 
mtum  aceeUfgm*  Pr«  oelabitur  filfbus  et  no« 
tabilt  qnapiam  attitttdtiie  in  fuqfeAQHi  pla« 
titim  molle^  e«  c$  m  jirgilUm}  tmprinwt  cavl* 

*  ta- 


d 


240    '  Siclib  it.  Cjput  trU 

C^rem.  Idcm  fi  ex  h-^ajori  alritudine,  \\t  dii* 
pla,  tcl  tripla  altcrius  deti^ittecur  ,  majorem 
cavitatcm  imprimec  j  quarc  fiiajoreni  habet 
quantitatem  motus  cx  altitudine  majori  de- 
lapfui»  quam  €  minori.  Sed  majorem  quan* 
ticatem  motus  habefe  nequit,  niii  in  defcenj^ 
augeatuf  C)iisdem  velocitas;  ergo^  tf\  fn^ 
Quatititas  motus  ^  MC.  Eft  porro/in  hypo* 
thefibus  noftris  eadem  nu^a,  cum  globus  idtni 
pon^tur  jam  t  majori  altitudine  deJabi>ja|n  < 
minorij  proinde  manente  n.afTa  eadem  de« 
bet  celtritas  globi  cafu  fecuhdo  crerccre ;  CN 
go,  Onf  Exptfiniefttis  GaliUi^  Rkskli^  di 
CtaUs,  Hi\vtoni^  aliorumquePbilofopborum  ab* 
undecxplofatum,  manitefte  imo  eviftutn  ha*» 
bemus :  corpofa  gravia  in  fuperficiem  tef rit 
delabcntia  motum  accelerare^ 

Schdl.  Qn*  iA  pofitioneif)  hafifc  6*pt)6ni  fblcftt,  da*- 
t)0  in  Scholio  11.  ad  §.  fcqaentcm.  Prhis  qtiantifarcm  ac- 
cclcratioiiis  cxpotiam.  Qyih  tero  pTopofitnm  mihi  cft 
ca  foliim  cxppticrc,  ifax  prjcCipo^in  m  Phyfica  tifuifl 
Jiabcht,  again  dufttaxat  dc  motti  'nniforrHittr  accelera- 
•to,  &  rctardatOrf 

§.  160.  tn  mtu  uniforfniulr  aMUr^U  fp4* 
tia  s  fnohilibus  dicurfa  fimt  ut  ^uadrata  tempo*^ 
rum ,  vel  Cfkritatuiti,  h.  ti  S  %  /  ^  TT  s  tt  :±i 
CC  i  cCi 

Sit  A*titti  A$c  (fig;  g.  j.   tWiAtm  fca«  M 

ijcfrimens  tttffpus ,  quo  motus  pcrdurat,  in  portioncs 
i|uetcunquc  «qqalcsi,  2,  5,  4,  &c.,  qujse  tcftipuftri* 
miiuma,' ac  ilifinit^  paiva  dcfignabunt.    Lihcjc  id,  ac,* 


i  . 


t>t  mtu  gtaviuml  s^f 

^ff  ASf  ^liftA^t  cel^ritfltes  Qngulis   temjliifcuiis  r<S- 
l^oiidemcfA     Jftfti  ii  ponio  temporis  ^  i  infinife  ptr» 
/va   ei\i  poterit  motcis  fauic  tempuictilo  refpondetis  pro 
itqtiab^li  hab^l  (ifititario  enlm  celeriratis  tempori  iti* 
finito  paH^  re(pondetis  non  nifi  ififinfre  parva  tSk  pO« 
teft);  igitor  fl  celeritas  cxprimatar  per  dit^  ipatiunt 
hoe  teifipii(c(i)0  confedum  exbibebitur  per  refiangu* 
um  Abdi  (  ^*  9 J*  Coroll.  )  ;  &  quoniam  /fi  eft  quan«   - 
litas  infinite  parva,  non  poteft  rethagnlnm  Abdi  dif^ 
ierre  quantitate  fiftita  ji  ^0'Ai\*  -    Idem  jodicium 
ifie^de  ttteris  refiibigulisi    Qutre  fi  lumma  refiangu« 
]|fr«m  omoiumi  etiam  tolnnl  ^idm  ABC  exliibebic  ' 
ipatittm  confed^om  toto  tempor«   ABy  modo  celeritaa 
in  6nk  temports   AB  aequifita   exprimatur  per   £C 
Efidem  ratione  /^lum  Ag4  refi^ret  i|totium  confefium 
temj^^e  A4,  &  fie  deinceptt     Hoc  poiito  iit  theor** 
ma  df mo0ftrai«r* .  *    /      ,        . 

*S'  >    *    •  •  •  1, 

'  Are*  tfiangulofiittj  4;4>  &  ^CB  func  in  [ 
ratione  cmpo^u  bajtum^  a^ Altimdinumy  proin<» 
de  etian:!  in  ratiom  dupUcau  ahitudinum »  vel . 
filarum  hapum  (  pef  GeomOi  «fgo  ifg4  /  ACU 
=  il4*  :  AB"^  s=  ^4*  J  C£%    Scd  Ag^  &  ifCil 
luht  rpatia ;  A4  kAB  (iint  tempera  j  ^4  &  CB' 
font  celeritates;  ergoin  motu  uniformiter  ac« 
celeraco  5  ;  /  sa  7T  ;  rr  t:^  CC  t  cc^ 

Corott.  t   Etiam  in  tnm  mifhmiter  retardata 

J^aiia  a  tHobilibUs  defcripta  Jiint  ut  quadrata  u^iforUm 
I  ad  ctUritatum*      Bemdnftr^tio   eadem  eft  qua^  antt* 
Sblum  celeritas  finalis  motus  accelerati  funienda  eft  p ro 
iCsIeritatc  initiali  monis  retardati<' 

CoHt.  It.  In  tflottt  unifdrmitef  dccelefito,  (k 
tifffpora  0c  ctkrHaufiL\x\mt  seqfiabilitet  iti  retift  ntinie' 
mum  natoralittni  i>  %i%^  4«  5i  <i  %  6u^    Quare  cutn 


S  f  tt^  n  lU^vtX  CC  i  ct^  crMt  ijitiii  «l 
rornm  iftonnn  qttadrata»  i,  4,  9^  16^  9f »  )6|  49,  &c. 
Sic  qnidein  (c  babcnt  fpctia  imc,  dmiim^  nUm^^ftmmtr 
ife.  tcfnporibcit  confccia,  At  Imfc  alit^  (k  Rabenc^ 
fi  CQm  temporibof  fiuffik  filiwrk  fitmfak  c^fcran* 
cdr ;  oti  ^nm  qncritQr :  qQcnmn  ^cfti  iMbilc  dtciir* 
rcrit  ftimo^  vct  iolo  Jf€mJ$^  ftto  iMjCi  fmrm  Iv* 


C^rotL  JtL  U  MM  m^^imimf  mctbm»  ^M^* 
s  mobiti  frpiUf  nmfufafkr  ^mfoB^  fim$  1»  fine  m  * 
maromm  imp4rium  %i  }»  fg  f^  A(&  id  cAi  fi.  1«^^  i'  • 

ilanti  mobik  dccwrfit  u  ^»«1* ,  Crim  Ccmmmio  ioftaM  dc- 
currct  podcs  crct»  tcriio  5»  qmio  7»fta  Navi  fi  mc* 
bile  intra  unam  tnt^  cfnfick  i.  pcAnn,  intfa  dno^ 
inftantia  4  jpcd.,  Coio  mdo  inftiDts  ^ODficicc  pcdc»  1  »-* 
I  =:  }•  Si  tntrt  duo  dccurrct  podc»  4»t|iirf  cria  ^; 
iblo  }!»•  inftanti  documct  pcdca  f  ••  4  »  f.  Si  intro 
Cria  emctituir  pedc»  5,  intra  ^tnor  16,  &I0  qoirta 
inftantt  cmciictar  j^cc  16  ^  f  ss  7.  P.  Hmrimi 
nutiam  fic  rcm  exptanatt  dcIabatQr  corpna  ./^  (ecoa* 
dam  dtridiMcm  Hnc»  ^D  ( FtgQr.  97.  } ,  prtmoqQe 
dcicMftit  inftaoti  Qnuoi  duntaxat  pcdcm  dccQrrat  ri 
cckrfttt|S»  aQcm  (nccciCve  acqQirin  Com  appnkrit  ad 
Mndiim  B,  five  «d  fincm  primi ,  &  isitiQm  &CQndi 
mftantti»  duos  bi^ebit  TclocitAtia  gradot)  altcrQm»  ^QCfH 
imo  tnftinti  •cfoificrat,  &  acqQifitum  dcinccpt  confier 
vat ;  altcrumy  qnem^  oAe  acqoirit»  Ex  rationc  primi 
duot  pedet  conficicty  cx.  ratione  iccQodt  itnQm  >  qQtre 
dQrante  (econclo  inftanti  tres  cmetietQr  pcdcs*  Cuni 
ed  punfhim  C  delatum  fiicrit,  (ivc  ad  fincm  &CQndi»  dc 
ioitium  tertit  tnftanriS)  tres  b^bcbantur  vclocttalit  gre» 
doi,  duo  quidcm  prius  acquifitt,  tcrtiui,qui  adu  tc« 
qQiritur.  Daobut  antc  acquifitit  decurrct  cbrpuss  4«^ 
pedet ;  ^tio »  qui  adlu  acquirttur,  unmn  ;  qwre  infttiak 
ti  }tio  dclabcnt  corpus  dcfcribit  $r  pcdcs« 


w 


Or 


« 


.  k 


tmTU  ty*  SfatHm  im  impvri  mm  UH^rmU 
m  melitM  ptrcmrfm  9fi  JkUtiflm  iBiui »  ^id  f  #« 
Mm  timpire  yirfurrmt  moiihi  fi  ^quakitiur  mpverts 
ntr  viMt0ti  iB4  ifttegra^  fmm  balnt  arfus  fpfi  mu. 
put  ifiuij  Cta  cf icritiw  fiifflU  motiis  tccctoteti  (loc 
«njm  cafii  deftrAtffC  t«0tf«tii»ttt  MCD  (  ^9}.  Cu^ 
tuVL  )  tM^  fM^ot  HHKti  ttiiiform^  iCeeUrtto  Ci&tip^ 
iertc  ^utti  i^SC  cjtistoN  Mti»  &^fltitadinii|  tt^au 
<ft  dtdtim  reftangiilttmi  ft4  t^lnm  htbent  etndem 
btfim,  &  iltira41ifMHii|  qttM  ffiai|tfi|ioiBf  eft  rnlNlupIttftl , 
iUittS  reOmgttU  i  «rgo« 

&i^.  F<  &  ^MQper^  iSrlefy  ikjkiuiinti^  m$tum* 

M  umfarmiw  ucuArmuif  irimiufis  mf$ifipi  fmu  ui 
tadkes  qmirtMi  §0ii9rm0»  Kum  (  ex  demonttrttis ) 
S'i  i  m  CC  i  ce\  ergo  ttli^ftto  «^trtbendo  rtdicem' 
qtttdrtttm  obthidkftttf?  Yit  tT^  «3  C  ^  e<  k  e.ve*> 
tocttifei  ieqt^ufc  Imii  ik  ridiiH  ^ttidrttfi^  <pitiorom# 

Ckreffi  $^4  iu  iiim  arpm  ompiru  fitnt  ut  rth 

itat  mtairatet  ^attirum^  fiir  perimtmttur*  Rurfiii 
miim 5  I  /  sa  TT  i  a^  dtttre  Y*  «  Y^**  -^  1  #« 

CerOi  m  Qm>  Y*  ^  Vl**  ^  t  <,Aitctutti 
YStYt:sti$,€6i  ($i  t- ut^4  IV4  Corolt  ^ 
C  j  e  »   T  t  /« 

CenU.  yitl^  St  iii  motti  tmlformiter  iceelihifi 
S  m  TTf  &f  m  ttf  etitm  hiliibitur  1  ^  t^^i  ^tii 
enim  etiim  creieom  «c  ilrci  ieeelerttrieet<  Sod  iit 
mota  tttiifermicer  ieccimio  tii  ieediritritt  eonflini 
cfti  fis  eotifiitti  miitiCii  ii^  ittfoi  focA}  cttm^O 
ttnita  nihil  mttlci^lioeCi  fhlvan  dicicttr  /  «I  ir«  In  mi' 
joribui  timen  difttnciji  mttUitttr  vii  iCceleriCritt;  ftMU 
ro  ttbl  di  iflSi  iq^kttr^  puti  itbtt  $  H  mt. 


j 


/ 


244,  Sc^U^  IL^Qfput  rh 


atott.  tX.  Qoii  /  53   vit,  fict  I.  —  =a  r.    VU    .     \ 

u 

i  f  -  '   • 

—  tt  ».    III.  Y  —  zz  ^ 

OhtoU:  X.  Quia  C  :  r  sa  .r  .w  C  Coi^oIL^VlL  )  ; 
ft  /^  vtt;  fa£U  (ttbftitutioQc  fiet  Iino^  /  ,i=  vc^     IL 

-^  a  i^.    lll.  —  ft  tfc    IV.  Y  ~  -  €» 

CC  '         V  i^ 

/-''.. 

Or9?;  XL  Qnk  vnirerft  «  9  ^-^|4c/s  vny 

f 

•btiiieiiftv  c  £:  .«-*  «  i«»  < 

JA^tfZ»  J.  Ex  |)is  i^mefida  eft  f^tulio  (^ufmriuni  > 
J^robleiDatmn  i  .  I.  J^ato  Jpatzo  a  cotfore  pritjio  nifian* 
ti  pcrcurfo  e.  c.  15.  pedum  invenirt  f^atium  quinqtie^ 
ntCtnenHs  fergtirrendum^  KevoCctor  proportio  S  ;  / 
ss  TT  :  tt.  Litteris  fiibfiituendo  numcros  fiet;  15« 
«a  I  t  2^.     Et  qu\A  fiBUtTi  midiorumVc.  habet^itpr 

*«   975- 

IL  Hafo  ^atto  a  eotpote  ptim  defcenfvs  iuflauii 
forcurfo  (  ij<  ped,  )  iuvenire  - JpaHum   fiinto  itfftanti 
ferct0'rendufn.      J^.  Spatia  fiugalis  tempnfculis  CQiifiKhi 
iunt  in    ^rie.  numcrorum  ifnpariiiHi  (^,  p^^J*  CoroU^   .. 
JII. );  nafcetur  icaquehsc  p^roportio  ij^  ;  «"ss  i  I  ^*     .4.4 
Si  1$'  du%ur  in  9^  cric  «  z^   \\^. 

III,  Dtfffl  ratione ,    ^ii*  bahetur  inur  Jpatia  pef^ 
eurfa  a  corpore  tnotim   unijoriniter  acceleraute  ^    detef- 
viitiare  rationttn  telochattuny  quibm  ikxc  Jpafia  percitr- 
fafueruuu    Corpus  A  dceurrem  15.  ped.,  corpu&  B  ^ 


/ 


Dc  moiu* graviumf  24 J 

*.37^'     Quonfam  (rcledtjitcs*  acqulfitJt  funt  nt  radicff 
**  qutdwisc  /patiorum  (  Coroll.  V..)^  nafcetur  proporti# 
C  t  <:  ;i:   vxj  i  YI7^     Sc4  VI5  «  Y$75»  W 
fir  4  '  19«  «rgo»  &  Q^lerl(atcji  rum  ut  i^ .;  19, 

ly/  Oo/a  ^4<£riii  mio)ie  ^ofUrtm  invpAit%  fmiu 
fiitff  umforum  Ui  iu  pircftrrepdtf  Jmpenjhr^m*  ^t 
]Etiam  tieiTipori  runt  at  radices  qaadrat^  (patiorom  ( (^ 
rp/f^  ^J.  }  ergo  fi  tempiis  impcarum  a  «corpore^;  cni 
|}edc8  15,  decurfl  tribuuntur,  dKratui*  T^.Si.nltpTiMSi 
cui  pcdes  375.  affignamur,  vocetur  1»  erit  T  1  a  j;is 
,Y^5  f  Y375»  Eft  Autem  Y^S-'  Y'l75t  &»  na 
4  ;  i9i  :;?  ji(H?  ci);»  fcrc  ut  1  t  s*  ergo, 

i^cio/.  IL  Ut  iidem  datam  liberem^  bbjeaionet  ad 
1«  1%^,  attiQCDtcs^  brpviter  config^abd.  .  O0ofi;  I.  Si 
in  defcenAi  grfvium  motus  acceleratui:  >  fallit  .J«i^  ^li 
univcrfalis;  eorpus  otnne  perfeyerAt  i»  fii^feu^qmiikt, 
.'fiyc  tttotus  uni/brmiter  in  direSum  \  fallere  autentiioil 
poteft;  crgo.     ]^.  Adjiciendfl{  efl;  l(»;i8  lAiua  risftridia 
a  Philofbpfais  omnibiis  rcccpta)    tUfi  a,  c^ufa  ixnantm 
cogatur  fimum  fiiwn  immutarem      Atque  cuid  bncvrt!» 
ftridione  fampta  lex  non  fallit.     Dicet:  nuUa  videtuo 
adeife  cauia  cxtrfinea»  quae  fliamm  corporum  de&eudfiiii 
tium,  immutet ;  qua?   cnim  ?    ^  £{l  graviuu  JmQi 
inertia ,  pcr  inertiam  retinet  corpos   feftundo  tCff^Qt . 
iculo  mo^um,    qu^m  piimo  inft^ti  acqiiifierat  ;^  pe% 
gravitatcn  det^rminatur  ^ad   motum  celeriu^  perageh<^ 
dum ,  cum  gravitas  pcndeat  ab  attcadiope  agente^^iii* 
rtitiohc  rcciprQca  duplioata  dif}:aptiari^ ;  biac  cum  in 
^eic^nfu  graviom  (ingulis/ tempunrulis  d^eicat  ^m^ 
^a^uni  didantia;.,  dcbe|  ^fuUs  {^pnCcoUs  crefeaMi 
e^c<^u$   gravitatis^   id  cft:.  ^tds  acaciarari   debet*  > 
l^i$es  ;io«    Atqui  grav.kas  Qoa  cft  caii(a  «Kjtrauea^^cufit 
fy,  matua  corpoj^ac^  attrafUo »  ergt  fi  corpor:^  ab  alto 
df Iab^ui4   motMM)  ^  a^(^ler|nt|  ff%  Ux   gcneiralis  de 
(oivTHtv^ad^  Aatu.       Wf.f ' An  .(rai^fat  corporibus 


1 


94^  StOh  tr^  Cmmt  Vl. 

triii(«»  fie,  iiv  intrin&ct,  myfteriuin  eft  Philo(o|liicitm  ; 
'M  neqae  de  ertraSipnc  ccrtum  cft»  flncme  «b  ipA 
'torporiim  natQrt,  iin  •  Kbcra  DEI  vohmCitc  pen^e^r. 
4ntcrc«i  mo,  quidqnid  horam  conftttnttinr,  (cmpcr  wx* 
(k  qocpma}  eorportbtit  nsomm ,  eecctcfMitHnic  csrruiee 
pTf  Ao  eft,  qos  tllem  ftetut  matationcm  indoett.  Stno 
l^rillieftt  eaoiam  ab  tttrtftionc  pcndcrc  dictm  Btrer|» 
^ovlnfo  \  fime  meft  tcK  OEI  ^  qt  corpom^  ifi  ccrttt  - 
4i(lliftiit  t«l  le  ft  tcccdapt,  cclcrittttbut  rttioiii  dircCte 
mtftMim^  rcdproetf  dopUcttB  diftantitram  rcQ^ondco* 
tHm,  etnfii  mottti  fttnn  corporibot  extrtn&ct  cft;  € 
tttil^io  propriitat  cft  eo^orftot  imrio&Ct  ^  tdlmc 
«taft  motnm  tcccieFtm  corporibot  extrinlcet  d)d  dc» 
bct ;  non  ctum  corpuy  prepier  fiitmmet  dcbbeoiit  t^ 
m^imcm  motiim  tccclert^  M  propier  elicntm» 

llf  In  motfk  nniftyrmitcr  tcceteratoftttit  ftngn» 
tti  Ctmp«(cofit  ftorfim  (qmptii  defcriptt  eft^t  in  ferio 
MfMvomm  imptrium  i,  ],  f,  %  ^.  (  Otfft  W^)f 
^jpmd  pogtuNre  videtor  ««im  t^e  titcrt  Nevtoniant ; 

CNitpat  tiKerf  dctcfndent  (ecmido  tciripu^coio  conficit 
mitilmii  Qmtii  cjas,  qjtod  primo  ttmpaicoto  deeorrcrtt,« 
mim  ftmcn  dopltm  duotaxtt  vclocitttcm  btbett  iiliaf» 
mim  primo  infttnri  obtUicbtl^  Atqui  iic  motat  non 
m  proportiontli$  ctuiSr  fu*  adgqate«  \  com  dopt«  vc* 
licmti  ttntommodo  duplctt  rc4>ondcrc  debcat^fiom ; 
mo,  ||e.  Ht  A.  Ad  Prob.  D,  M,  Corpat  deiceiidcnt 
lecnndo  tcmpo(cato  dopltm  donttxtt  velocitttem  ^ 
rtner,  qatm  titbacrit  prim^»,  e^m  ttmen  uti  jHmti  fio 
y^iitft  tfcm^oicohi  crefimm  C»  M«  Cotifiiamm^  & 
•fotbiicm  I*.  Mt  Sio  D,  m,  dc  N,  C,  Si  celcriflit 
teMcrmorof  icqniift  conHtnii  eiTct,  €f  <rqiiti>i>ss»  n^ 
^t  ttit  c^itas  facccflhrc  iccedcrct ,  non  poftee  mo* 
bttc  cclcririte  dnphi  nid  doplom  ^tium  eoofioert 
Cnioi  fl  r m  r,  cft  Ci  c  ai  S  t  V P«?otndc  C se  ^ H' 
que  tdeo  tC  ai  iS).  .'At  non  itt  m  ft  Ubet  inmo« 


l 


y«A  >&iM  •tmportt  iK^^^sft^  k^^'^  ceferiMp  qaai» 
focric  fiib  tjiiaisitfa^^iS^  |^  trcloctMtt  (ab  fi-^ 

nein  cempoiit  primnicqaiiTrtf  flcslinertitiii  eonlcr* 
,rira  moyctar  corpot  tempoicul^.l|ei^do,  jamfM  vi 
liQjut  dapUvm  (pttti  prtoris  eonflctif)^  dcbcf .  Sc4  Wn* 
pa(cuto  fifciiitido  iterom'  incr efcit  oclcrirtt ;  qotft  pnc- 
ter  incrcmehtam  ccicrirtHs  in  fiic  limports  pcimi  cc- 
qailimm,  dcnoo  (bcccflitrc  tccedcrc  dcbcc  noVaOI  Iq^ 
mcncam,  cuaiqoo  motds  poofcor  anifbraiter  oiedcci- 
ttis  incrcmcntam  illnd  priori  «qoclc  fir,,  oporiic ;  qoo# 
re  (ab  flnem  tcmporis  ficcindi  eelieriiis  non  doplc  o?t« 
dct,  fed  triplc;  hinc  ittdcm  mobtlc  ooa.dophim^  61 
friplom  prioris  QKtciom  confidct* 

IIL  InconciPtibile  eft;  qaomodo  ^tte  oiota  ii«; 
celerato  confedi  fint^  ttt  numc^i  sb  oiiiMe  rmparcs»  t, 
>3i  S*»  7f  ^c*  Prioio  enim  inftanii  voloeit«tt  acooifica 
dccurrctur  rpttiam  s  i.  VdooiM  iidcm  pc|(cvcri* 
bit|in(lanri  (ccando,  perqae  iAam  dceocrctor  itoraoi 
fpaciom  s;  I ;  (cd  qota  nonM  rdodtitts  grcdos  i^ 
dit|  qui  pcr  idem  inftans  fccundo  eonfie&r  rpctfam 
t:;  i\  proptcr  duplicem  illtm  vdodteccm  ewfirxmmn 
(cilicety  Ol  mvifir  $tcrefi0Uim ,  (pctium  mn  mpbm 
percttrrctur,  (cd  umtmm^o  duplum;  prg^  ^a$U  fm^ 
piUf  infitmmm  mfi^  «co  fim  in  firii  mnHrwmm 
imfgrmn  i,  |,  f,  %  &^.,  fid  iufirit  utintralmm  l»  Sp 
3,  4,  &c.  if*  Objcdio  b«c  eadcm  cft,  qncjmas ;  qoar» 
cadcm  rc(pon{ionc  cxpcdiri  potiell. .  Juverit  fortc  inccr 
tcmpafcola  iu/lftif*  piroc,  (k  fiuitg  cnm  qaibosdam  ao*' 
Cloribns  diftinxiflc.  Stc  illt  i  (patium  decurfiim  (ccon^ 
doinftaotif/;j{otie  jMrocduntaxat  duplum  cft  Q)atit  coii» 
firftt  iffi  primo  int»ttti  itideni  iufiuit^  parvo ;  naai  pcf 

Ciniini  tnftcas  aatcos  tantum  velocitatis  gradus  habcw 
iir,  qoi  fi^cundo  inifamtt  pcr(Werat  qoidcm;  G^  alia 
iU^us,    At  nbi  inffaincia  (ttnt  finita  ^  icontinuol  mobilo 
/ifl  pritfri  nmfufiuH  fimm  fit^effivt  arqoiccrc  pott  ft_ 

Q4        •  & 


•• 


S4S    ,         &8ion.  tUfmtVL 

0C  T9  rqt^fite^tffive  acquirit  novum  vclodliti^yrijiam ; 

fic  pi^oiilde  pofl:  tetnpu^nluin  primuni  inovitur  velati 
'  cum  cumnlo  plurium  velocitatis  graduuro,  quos  ua* 
^uam  fimul  habult;  quamvis  igitur  mobile  nuUuOi  dein« 
*  ceps  acqaireret  valocitatis  incrementum  pofttempufca* 
lum  primgm  movcretur  tamen  velocios,  ipatiumqae 
majus  condcerct  tempu&olo  (ocundo »  qoam  primo  U» 
cet  zquali ;  ergo  cum  eorpus  tempu&ulo  illo  (econdo 
novum  acquirat  velocitatis  incremcntuoi,  non  dapluai^ 
M  tripUim  prioris  Q>atium  conficict, 

IV,  Motu$  illius  «cceleratl  caufii   eflbt  •ttndio; 

'  qua  confticutii  rgddi  nequit  ratio,  cur  iu  VMw  Beyhn^ 
coTpor^  molc,'&^  maffi  omnino  dii^rCi  tsmen  eadem  ad 
fenfum  velocitate  dcfccndant,  Sane  cx  Ntmtom  prhi^ 
$ipiu  mancntc  cadem  caufi  m^nero  dcbct  cffeQus  idcm; 
proinde  cum  •rtradlio  terrar  CAdcm  babeiitur  extre  va« 
i  cuum,  qus  in  vacno,  utrobiqqe  corpora  utcunque  di« 
verfieademad  fenfiim  cclcritatc  delabi  dcbercnti  quod 
ttmen  quemadmodnm  non  fiat,  expcricntia  ccrtum  ba* 
{)emus ;  nam  cxhaufto  a$re  ex  rccipicnte  ^.  pcdcs  alto 

^ohuf  piumbcus^  &  ligneus  eadcm  cclcritatc  defcen- 
dnne;  at  a€re  immiflb  infigiie  ccicrirati?  difcrimenadr 

•  i^rtitar.  ^j,  Eadem  cft  artraaio  terr«  e^tja  vacuum, 
i|U2  in  vacuo,  diverfa  tamcn  efl  rcnflentia  mediii  qoam 
corpus  labens  (upei^are  dcbct  C.  A,  Et  eadcm-  cft  rc» 
liftenria  N.  A,  &  G.  m,  exhaufto  a«rc  nihfl  cft  in  rc- 
cipiente,  quod  corporibus  ex  eadem  altitudine  dcLabenf. 
•  tibuf  (enfiMHtcr  rcf?ftat,  motumque  impediat;  ergo  at* 
quali  ccleritate  dcfccndcnt  corpora  vcrfus  tcrram,  A^- 
re  immifTo,  qul  corpornm  motni  ftnfibilitcr  rcfiftiti^ 
fcnfibtll  ceierltatum  diftrlmine  fcrcntur  corpora  verfus 
terram ;  magis  enim  rcGftit  acr  corpori  (pccific^  Icvio» 
-    ri,  quam  graviori, 

V.  Sl  in  vacoo  Boylcano  nulla  bnbetur  fenfibiUa 
medii  refiftcntla^  dcbcnt  iu  <9dm  vmo  cerpora  divcc* 

fif 


•• 


f 

Dd  mfftu  gravium^  549 

fir  graviuiif  {pecificx  divcr(a  etiam  eekriMeideljbi; 
/ed  not^  deUbnnrur  \  ergo.  Pr,  M»  Artraf^iones  non 
Riodo  funt  in  ratione  rcciproea  duplicara  dii\antiaram, 

.  ied  etiatn  iti  dire6^a  ivanaram;  ergo  corpna  ipetifiec 
grai^ius  majori  veldcitate  deleefider,  ^nam  fpeeifiet  lei» 
vius;  proinde.     ^.  Attraftiones  funt  in  ratione  fimol 

-  dir^aa  maffarum  amabmwm  Ci»  A.  at$raff0rrmS.  Af 
^  C.  iP,  ^qoaii  defcenfiii  non  otficit  diverfii  gravi» 
tas  fpecifica,  modo  eadem  hakearvr  mafla  «nrii^iM^nalt 

.  laque  (qbfit  impeditio,  ' 

Vlt  Pofita  eadtfn  tnajfa  anrahenUy  &  afaali  mptui 

imfedhimt  deberent  co«|>ora  diver(c  gravitatis  fpecifi* 

ex  ex  eadem  alritudine  demKTa  eadem  ceieritate  ferri 

verfUs  terram  aiam  etttra  vacunnt  $oybauum  (fiqui* 

. derH  acceleratio  mociuoende^t  ab  artmfiioaft  mtx,  pro 

|-atione  diflanriarnm  (e^6  cxcrcnrejr;  iftnd  vcro  pu* 

,^nar  cum  obiervattombua;  nam  capianir  globut  fev» 

reua  alter,  alter  ligneii»  parit  ^qaidcm  dianerri,  (oi'  ob 

Viis*    £x  eadcm  idrirndiiie.demifli  ambo  pari  ceterita« 

te  non  defcendent;  prcvalebic  cderkaa  ferrei;  ergo« 

Pr,  M*  Si  extva  vacnum  non  habetar  arqualis  oeieritcs 

.corporum  derveiidenrium    in  terram,  insquaiftaa  iiit 

repetenda  eft  a  Coh  medii  refiftentis  impcditienc;  ct-» 

go  cx  oppofito<ubi  squaiia  babetur  impeditio,  dehene 

corpora  diverf^  graviutis  fpecifica^eadem  celeritatede* 

/cendcre.       Sed  pari  voiamini  g!i!»boeum  ierrei ,  &  li* 

gnei  refpondet  par  volumen  aeria ,  proindeque  par  im« 

pedirio;  «a-go.     jgji.  N,  feqnel.  M.     Ad  Prob.  D.  C. 

pbi  squalls  habtf  ur  iinpeditio,  fiinulque  par  nicdii  re* 

fifientis  vicloriay  ^  eeque  fofilis  fuftraM^  defcendnnt 

corpora    diverCe  gravitatis  ^ecificr  eadem  velocltata 

C  C.      Secus  N.  A.  &  C.       Vieloria  mcdii  refificntit 

non  modo  pcnder  %  dcnfiute^  rei  quantirare  medii,  (ed 

&  a  denfitatc  corporia  medtum  fubingtedienris ;  fingu* 

\^  enim  moleenic  mobilc  componenres  nitumiir  ad« 

}I^vCm  mcdioo)  f efifleiis ;  crgo  qip  plures  ftterint  mo* 


3JO  ^BwIUdfmVL 

lecuU»,  tm  <|iio  maiM  fuerit  corporis  nm\  pm«ltit 
(bb  oorto  «iiqao  vdlumine,  hec  prompttQs  fuperabtttir 
xefiftentia  medtt ;  quare  corpors  diverGr  gravicatis  jjtcw 
dfim  \n  mcmi  oonftitait  extra  vacooni  instqaiti  cete- 
ritate  de&endcrc  debcilt. 

VII*  S^tpc  eorpora  diverfie  gravitatis  (pccificx  (  & 
litiic  diverfi  quidem  ponderis,  fed  ejttsdem  volaminis  ) 
eadem  ed  Anfam  celeritate  dcfcendant.  Sic  mafla  ao^ 
ri,  &  maflfa  Mercarii  paris  voluminis  cx  eadem  ahita* 
dine  li  demittentor,  eadem  ad  renfum  vclocirate  de(ccil« 
dcnt;  ergo  promptior,  ae  facilior  medti  refiftentfs  (ii* 
peratio  niliil  edmodum  cohfcrt  ad  insqoalitatem  cele« 
ritatis  in  de(cen(ii  graviom.  1(2.  D.  A.  Corpora  di- 
vcrlc  gravitatis  (pecificdt  etiam  extre  vacuum  eadem 
velocitatc  dcCceiidttor,  (i  diiTercnria  ponderis  (it  admo* 
dom  magaaN*  A»  Si  non  omnino  &uhd.  eadem  (enfl* 
biliter  velociutc  C  A«  re  ip(a  etiam  in(en(ibilirer  N.  A. 
4c  C.  m.  Si  ad  refiftentiam  inedii  cehrrime  fupermm 
4Um  rcqairitur  certum,  ac  detcrminatum  pondus  quod* 
piam  corporis  de(cendencts ,  dooqoe  corpora  per  idem 
iBcdiam  ex  eadem  eltttadine  delabentia  pondus  illad 
•ttigci^int,  cqo^ii  celerltate  de(cendmi^,  quamvis  iflo» 
rom  alteram  excedat  in  pondere  ad  rcfiftcntiam  medti 
ctkrrime  (apcrandam  reqoi(ito;  nihii  enim  exccirat  it- 
le  opcrabitor  habita  ^m  celeritace  (enfibiliter  fumma* 
Pono :  to.  libris  celerrime  fuperari  re()ftcntiam  acris 
modico  voiumine  rcfiftentis*,  (i  corpos  aliud  i^*  tibras 
appendens  ex  cadem  tlritadinc  delabetur,  celertus  medii 
cjusdem  re(iftentiam  (uperare  non  poterjt;  quar^  ea« 
dem  vclocitate  delabetar,  qoa  corpus  lo.  Hbras  appco*^ 
dens.  Similitcr  modics  maflTc  ejnsdem  voiuminis ,  Oc 
non  mulrum  divcrfi  pondcris  aeqnali  eeleriratf  ferri  poC 
bxm  verfus  terram,  quamvis  eonindem  graviras  abfoha* 
ta  non  (ufRciat  rcflftentiar  inedii  eelcrriinc  A}perand«; 
Sum,  qood  modicus  iilc  eKceflfus  in  gravitatc  abfoiota 
viK  rubica(usnoftr9sc«dar»tttm  qaodmcmorata  dfiycr^ 


Jh  motu  gtsvium.  f  ]  f 

litas  pondcrig  •Ufer  cofnpcnfiri  poteft.  Noi^^:  r«(v 
fteium  fivc  inipcditio  auidoruin  c  4-  capitibm  ptoflttit 
1  mo,  A  fluidi  dcnfitate.  ado.  Ab  'ejusdem  tcoftritate, 
&  vifcofitate.  Jtio.  A  corporis  iocttrreiitit  fuperiicio. 
4to,  Ab  cjusdcm  vclocitate.  Atqu«  poitrema  quidcfn 
iUaiinpcdittonis  origo  hoc  loco  recenlcnda  non  eft,  «um ' 
de  ifta  lis  fit.  Quid  tamen»  fi  corporis  umus  denfit^ 
cgregic  compcnfctur  pcr  •Iterius  ftipcrficiem  infigmter 
*l«vigataro  ?  Sit  globus  ferreus,  &  ligncus.  Ferreos  fu» 
pcrficic  i^fpcra  i  ligneus  polita,  &  glabra.  Immo  U  ^i« 
ctiam  fcftuc«  in  lignco.prominebunt,  faciie  pcr  affir»r 
fium  inflcacntur.  Potcrit  crgo  iompenfatio  quatdam 
lubcri  fic,  ut  quamo  plus  a«Jr  impedicrit  Ugneum,  quam 
fcrrcom  AeQata  ratiQm  fuitrii ,  t»nto  ampUoi  in?pc# 
diAt  fcrreum,  quam  Ugncum  Jjb*atfr4  raHofH  Juptrficifi 
afier^e,  An  non  «qMilU  fict  refiftcntie ,  tc  impcditio 
fluidi  ? 

Quanqnam  ingenue  cpnfitendum  eft,  vijt  c«rd 
quldquam  bac  in  matcria  conftitui  a  nobis  poffc,  cum 
cuaorum  divcrforum  experimcnja  non  fitis  confcJl» 
tiant,  Vulgatum  eft  illud  DfJaguUerih  qui  prafenti^ 
bus  Nwefw  aUisquo  Uttcratis  fene  homimbus  e  turr* 
tondincnfi  Oiv»  f««/i  %7%.  pcdcs  alta  divcrf*  gravi* 
faiis  fpccificat  corpora  demifit*  Compertum  eft  ob* 
fervationibuf  itcratis ,  quod  corpora  travitati  fua  rcli- 
Qa  non  defccndcrint  cadcm  cclcritaic,  nequc  immo  co- 
rum  dcfccnfos  ficbat  in  ratione  gravitatum  fpecificarum. 
AUi  contra  aflirmant^  globos  divcrfi  utcunque  pondc» 
ris  ab  eadem  alcitudine  alibi  dcmiObi  «que  volociter 
in  tcrr^m  deJatos  fuiffc. 

VIII.  Qoo  mtjw  celcriwf ,  1i«c  in«jor  in  wdcm 
imflSi  qtwntitu  rnotu* ;  qnare  corporom  ex  pr«grandi 
•liqaa  •Ititodtne  dcUbwttivn  admodum  magt»  cflc  tic- 
bw  aaantitM  mon».  Ttlcm  vcro  oon  «xpcr»mur  ii» 
«iribtt^  piom,  |fwltM  &c.  91)9  coro  cs  ipto  wttbmro 

•%  aS» 


/" 


--T\ 


' 


15^  ^^^'^  Jf*  C^P^^  ^'* 

.   «Itugdine  in  tctrx  (upcrficieni  dcfcrdnttir,  nihilominiis 
•xigua    niotus  quftntitate,  (ine  damno,  &  noxa  frugiim 
defcruntnr ,  qua  tamen  ck  pcrpctuo  vclociraris   ir.rrc- 
menro  confequi  nccenum  forct.     Vjt'  Suos-  accclcratio* 
nl  limltes  ponunt   Phiioftphorum  nonnullit  aiii  pofl: 
Juifiuios,  poft  treceittds  pcdcs  alu  motum  non  ultra  dc» 
celcrari  exiltimant.       Sique  motus  acceieratio  flibindg^ 
deiinit,  ajuntt  nec  ingens  illa  motus  quantitas  confiirv- 
get,  ncque  mctncnda  illa  damna  crcabuntur.       ^,  Ih  . 
Nix,  pUma,  grando  &c.  iine  frngum  Boxa  ad  nos  de- 
feruntiir,  quta  (cilicet  acccleratio ,   &  major  quantitat       .  ^; 
motus  continuo  impediatur  per  acris  refiifenriam,  qui 
perpetuo  aliquid  de  novitcr  accepto  velocitatis    incrc»      ' 
mcnto  decerpir.     Hinc  D,  A.  nix»  pluvia,  grando  &c, 
ingcntia  damna  crearent,    niii  quid   legltims  aceelert- 
tioni  motus  obftarct  fcnfibiliter  C.  A.  cum  phitet  aer| 
&  hoc  magis  obfict,  quo  corpora  delabentia  propiora 
fiirnt  fuperficiei  tcrr*  (  nam  quo  propior  eft  aer  fuper» 
fidel  tcrrae,  hoc  cftdenfior)  N.  A.  6c  C.      Ifta  aerls 
tcfiftentia  Divinam  Crcatoris  Saplentiam  infigniter  com- 
n-^endat.     Ncminem  latcre  puto,  quantum  ad  terrae  fer- 
tilitatcm  commodet  pluvia#      Atqui  vero  fublatg  a^ri$ 
rcfiftentia  adco  commodaret  nihil,  ut  potius  rclocifiitno 
cafii  fuo  ptffiQmdarct  omnia,  tcrramquc  produccndis 
fru£Vibus  inepram  redderct.     Quod  dc  grandine  addi- 
tur,  cjus  quJdcm  «ppofitum  &pe  moefti ,   ac  gcmentfi  ^ 
incuiti  (lunus. 

Parergon. 

De  caufa  graviutis. 

\^.  *l6l.  LineamdjreAxonts  aravium^qua 
ad  horizontem  noftrum,  five  foperficiem  ttr* 
r«  libere  jdeferuntur,  pcrpendieiilarem  e(fe, 

phx- 


•         V 


■^— n 


;. 


^H^ehoinenon  eft  quotidianiim  i  %c  irulgo  no^ 
tillimum;  femper  gravia  (nifi  duplfci,e.  c 
fhliqu/t  projtliioms  |  &  gravitAtis  vi  iirgeantur) 
cafu  fuo  defcribunr  lineam  perpendiGularem. 
At  de  pharnorticni  hujus  caafa  non  convcnic 
Jnter  Phllorophos.  Vari«  ad  hanc  materiam 
recitantur  variorum  auSoram  opiniones.  No« 
biliifimay  ac  fere  ubivis  jam  civirate  donaca 
efi  illa  Nttsnoni  caufam  grayitans  ab  attra^io* 
ne  repctcntis  Cententia. 

■  i 

ScboL  Taceo  Feripat^iiccys^  qnl  gi^avftfitcfm,  aat  po- 

tias  giavium  defceftfum  s  prtncipio ,  nefcio  qao  ,  cor- 

p&nbiisintrinfcco  fortc  a  Syrhpbatia,  Cew  iitclinati&ne  ali- 

^ua,  <jua  corpora  vcrfus  ccnefttm  terra  wrgeantwr,  rc- 

petendam  cffef  cen(ucrunf« 

Omitto  Qaffendunfy  tjti$qvie  feSf^eorcs,  e  qirorum 
{•nteitda  rerra  non  abfimiHs  eft  ingenti  caipiam  magne* 
ti^  e  quo  iogicer  crumpiim  irtomornm  efflnvia.  Has 
porro  atamos,  ctftcfwrum  vcl  amitilorum  inftar  ftht  cow 
pciUtas,  comminifcuntnr  uncis  fnis  rrabere  obvia  cor«» 
pora,  &  ail  deicen&m  eogere.  Gemin^  hafce  fcntcvu 
m$  vct  innuifTe,  ptitOy  refutavifTc  eft. 

CMrtefium^  6c  ^ut  hoc  dtice  mHitmt^  prsrerfre  ne« 
qneo.  Volunt  ifti  gravitatem  oriri  ab  imptilfionc  fiwi* 
di  cujuspiam  fuhtiltilimi  terram  imdiquc  ambienfiSy 
'  fuod  ipflim  grave  non  fit,  fcd  trniTcn  cauGt  gravitatis; 
Itque  iQ  co  confcntiunt  omnes«  Cirea  vere  fhiidi  iU 
Hus  naturam,  &  modum,  qno  gravitatcm  eorporuin 
operatur  ^  non  «que  il^is  convenir.  Dabo  CartetTaTto^ 
rofn  dogma  conceptis  s  Philofopho  quodam  Gallo  ver« 
bis,  cujus  nomen  non  rcpcvio;  iic  illct  Cartefitts  iftud 
tofifljtuit ;  vortex  matcri^e  fabtftfr  terram  amhit ,  ud  in^ 
^entem  atthttdtmm  fa^ra  terram  ajfurgit^     Vohipnr  vor^ 

^  teoQ 


3fo  SfSmir.  Ctfm  VT. 

faenl^,  Art  q«o  «ai«s  fiicrit  fiorforis  nad  panfct 
fiifc  e«co  flli^pio  voliuoAc,  hoe  prompdtts  fiipcnbiror 
xcfiflmM  «edii;  qosrc  corpon  divcrfr  (rniviratisjfiOi 
€^at  in  flioco  oooftitBii  cxcra  VBcmioi  inx^Mii  cdo- 
nCsto  ocicoBflcvo  ocbsnt» 

Vn*  &rpc  eorpoca  divcrfir  grs^tstis  Qwdficx  (  & 
kffic  dircrfi  qoiilcoi  pondcris,  fed  ^osdcoi  Tofauniius  ) 
Oidcoi  od  €mCmm  celcritste  dc(ccndiinr.  ^c  mMtk  so^ 
ri»  dc  msfls  Mcreorii  psris  rolomtnii  cx  esdcm  shito* 
dtnc  fi  dcmittcntor,  csdcm  sd  fcnfUm  irciodtscc  dc(oeo* 
denr;  crgo  promptior»  se  fsrilior  mcdii  rcfiftentis  (ii» 
pcrstio  nihil  sdmodnm  colifcrt  ad  incfoslitatem  cclc« 
ritttis  in  dofissnfii  grariom.  ^.  D.  A.  Corpora  d{« 
vcrik  gtaritBCis  &ocificjt  ctiam  cscio  vseuam  csdcm 
veloeit^  dsfimmiir,  fi  dtlGMncia  ponderis  fit  admo» 
dom  «sgiu  N*  A*  Si  oon  omnino  Smhd.  cadem  (ettfi* 
biliter  rolocitstc  ۥ  A#  ro  ipA  otiam  in(enfibiliter  N.  A. 
4t  C.  m.  Si  sd  BofiftsQtiam  osedii  uhrrhm  Jmpermu 
4sm  rfqtMritnr  certam,  ao  detormiiiatQm  pondos  qood* 
piam  corporii  d^cendcmis,  dooqoe  corpors  per  idem 
mcdiam  ex  esdem  atcitadtnc  delabentia  poiHias  illod 
otrigeriat,  «qtnili  eeleritste  de&endonr,  qusmris  ifto* 
ram  alcaram  excedat  in  pondere  sd  rciMeotfim  medK 
mhrrum  ibpofandsm  reqoifito;  nihil  enim  execflrai  il* 
k  operabtror  faabiis  |sm  celeritate  ftnfibiiitcr  (ommi* 
Pono  t  f  o.  itbris  ctUrrkm  fopcrsri  refiftcntiam  sl^ris 
modico  rolomine  refiftcntif ;  fi  ci»rpof  sliod  15«  librss 
appendens  ex  eadem  akitadiito  delsbctur,  cWrrto  medti 
^of dem  refiftentism  fiipersre  non  poterit  >  qasrt  m* 
dem  relocitste  delabetary  qoa  corpus  10.  libras  sppcti^ 
dens.  Similtter  modicc  maflc  cjQidem  voluminis »  & 
nonmultum  dttrerfi  ponderis  eqosrt  eeleritare  ferri  po(^ 
ioiit  rerfiis  terram,  quamvis  eoraiKkm  graviras  ab(bli)« 
ea  non  (ufRcisi  refiftmititr  mcdti  ederriine  (uperandtr; 
tum,  quod  modicus  ilte  e«ceftiis  in  grsvicatc  abrolara 
via  rt)bAn(ttfi}ofti:«i^B9i4^9taia  qoodmeittorata  di^er^ 


*   *  . 


X>#  motu  gtavium.         '       f  1 1 

Ctas  pmclcrif  alifer  compenlari  potcft.  NMft;  r9& 
ftentia  (ivc  impeditio  fluidorum  e  4.  capiiibiu  profloic 
imo,  A  fluidi  dcnfitate.  ido.  Ab^ejttsdem  tcoarirate^ 
&  vii!co(itate.  Jtto.  A  eorporis  ioeurrfutta  rupcrikiak. 
.4to»  Ab  ejnsdem  veiocitare.  Atquc  jpolkfiiM  quidcra 
iUaimpcditionia  origo  hoc  loco  rccenicnJanoncftiCum' 
dc  ifta  lia  fir*  Quid  tamcn^  fi  eorporis  oniua  dcnfitas 
cgregie  compcn(etur  pcr  altcri^  (qpcrficicm  infignitcr 
laevigatam  ?  Sitglobus  ferreus,  &  ligneus.  Pcrrciis  fii» 
pcriicic  atpcra ;  lignc us  polita^  ft  glabra.  Imino  ii  qom 
Ctiam  fcftucc  inUgnco^protoincbunt,  facilc  per  affrtf 
Qum  infleAcnror.  Potcrit  ergo  oompcnfatio  ^u«dam 
babcri  Cc^  ut  quamo  piot  a^  impcdierit  Ugncum,  qtiam 
fcrrcom  ^iQaiM  r0$iw$  paikfrr# »  tonto  amplioc  ifQpc* 
4iAr  fcrrcom,  qoam  ligncumjJkAcro  ruimii  Jvptrfidri 
^j^nr*  Aa  non  Moolis  fict  rcfiftcntio »  w  impcditio 
floidi? 

Quanooam  iaganuc  cooSrcndum  cft ,  rtK  rcrdl 
qoidquam  bcc  in  matcria  conftitoi  a  nobis  poflc,  eon» 
oudorom  dircribrum  cxpcrimen;a  non  fiitis  confcfi» 
tiantr  Vulgatum  cft  allud  D^am$Uirii%  qoi  pr«(entt« 
bos  Hemmo  alitsaoo  littcratis  lanc  bominibos  c  turri 
t«ondincnfi  J>M  rmJi  aya,  pcdcs  .alta  divcrfir  gravia 
tatis  fpccifies  corpora  dcmifit.  Compcrtum  cft  ob# 
(crvationiboa  itcmtis ,  quoil  corpow  gravitati  fuai  rcli* 
da  non  dc(ccndcrim  cadcm  eclcritaiCi  ncquc  immo  co« 
rom  dc(ccnfi)s  ficbat  in  rartooc  gravitatom  ^ccificarum* 
Alti  contra  affirmant|  globos  divcrfi  utcunquc  pondc* 
ftsak  cadom  cititodinc  alibi  ^fmKTos  cqwe  volocittr 
jn  Htfkm  dclctos  fniflc. 

VIII.  Qqo  ma)or  celcritas»  Imc  ni«)or  in  cadcm 
snalft  qoentitas  motua ;  ^iocrc  corporom  t%  pr^grandi 
iU§aa  attitodin^  iMm/A^  admodum  magna  cflc  dc« 
b#t  qoamiias  momi.  Tdcm  rcm  ntm  t xpcriimir  iit 
irinbo%  fkm^  mmdkm  &c.  qo»  €om  n  ipft  mbinoi 


•  • 


«5*  &^io  If.  Caput  PU 

fttritudiiie  in  terr^  fiiperficieni  defcranttir,  nihilonriinus 

txigua   niotus  quantitate,  (ine  damno/ &  noxa  frugnm 

•dcfercmrnr ,  q««  tamen  ck  perpetuo  vclocitaris  incrc* 

inento  confequi  neceflum  foret.     ^.  Suof-  accclcratio- 

nl  limites  ponunt   Phiio(bphornm  nonnullit  alii  poft 

diiifiuios,  poft  trecenw  pedes  alu  motum  non  ultr«  fc* 

ctlersri  exilHmant.       Siqne  motus  acceleratio  (iibind? 

definit,  ajuntt  riee  ingens  itta  motus  quantitas  confvir*'- 

get,  neque  metnenda  illa  damna  creabuntnr.      ^^  If,. 

Kix,  pUivia;  grando  &c.  itne.  frngvim  noxa  ad  nos  de» 

feruntiir,  qni^  (citicet  acceferatfo ,   &  maji>r  quantitat 

motus  continuo  impedistur  per  ai^ris  refiifcntiam,  q^ 

perpetuo  dliquid  dc  noviter  accepto  veiodtaris   incre* 

mento  deccrpir.     Hi»c  D,  A.  nix,  pluvia,  ^rando  &c» 

ingentia  damna  crearent,   nifl  qnid   legitimaE  accclert- 

tloni  mdtus  obftaret  fenfibiliter  C.  A.  cum  phftet  aer, 

&  hoc  magis  ol)ftet,  qoo  corpora  delabentia  propinrA 

firnt  fiipcrficiei  terr»  (  nam  auo  prppior  efl:  aer  fuper.» 

ftiel  terr«,  hoc  cftdcnfior)  N.  A.  &  C.      Ifta  acrls 

f cliftentia  Divinam  Crcatoris  Sapientiam  infignirer  com- 

li^^cndat.     Neminenj  latere  puto,  qnantnm  adtcrra  fer- 

tilitatem  commodet  pluvia#      Atqui  vero  fublatg  a^ri^ 

reiiftentia  adeo  commodaret  nihil,  ut  potius  vclociflilino 

^afti  fiio  pdromdarct  omnia ,  terramque  producendis 

fru£iibus  inepram  rcdderct.     Quod  de  grandine  addi- 

tnr,  ejus  qufdcm  tppofitum  {zpe  moefti/  ae  gctneotc|> 

intuiti  (lunns. 


Parergom         \:  :'\ 

.  De  caufa  gravjutis. 

td  horizonrem  no&rufn,  five  fiiperficiem  ter- 
r«  libere  jddferimrtir,  pcfpcfndiiuJan^nv  effe,* 

ph«- 


.* 


;. 


jpl^tiomtnoii  eft  quottdianism  9  $c  irulgo  no^ 
tiffimum;  femper  gravii  (nifi  duplfci,e.  c« 
0bli^U/t  projeBidfiif  ^  &  gravitAtis  vi  urgeancur) 
C^fu  fuo  defcribunr  lineam  pcrpendicuJarem» 
Atde  pharnomcni  hujiis  caufa  non  convcnit 
inter  Philofophos,  Varijc  ad  hanc  materiam 
recitantur  variorum  au^orom  opiniones.  No« 
biUifima,  ajc  fcre  ubivis  jam  civtrate.  donaca 
•fi  illa  Nflptom  caufam  graritacis  ab  accradio* 
ne  repctcntis  (ententia. 

Sckol  Tacco  Feripauticfyf^  <jn}  gi^avftatcfin,  aot  po- 

tias  graviutn  defceftfum  s  principio ,  nefcio  quo ,  cor-* 

poribusrntrinfcco  fortc  a  Sympbatia,  fevi  imlinau&ne  ali- 

^ia,  <|ua  corfrora  verfus  ccnBram  tcvrs  vrgeantttr,  rcr. 

petcndafti  cflTe  centucninr* 

Omirto  Q^iHdmmyt^sqjiie  {dfilstorcs,  e  quroram 
fifmsndar  rerfft  non  abin^ilis  eft  ingenti  cuiyiam  magne- 
M^  e  ^o^egiter  crampwnt  irtenfiorom  efiinvia.  Has 
.  porro  atomos,  ratenttrum  vet  amitiloriim  fiiftar  fthi  co^ 
pnktas,.  cofRmimfcunnir  «ncts  ftiis  tfjlhercr  obvifi  cor-* 
pera,  &  a4  Mkmfim  cogere.  Geminj»  bafcc  iemeii« 
tiM  vci  innniflTe,  pttto»  refutaviflfe  e&  \ 

Otnefiuf»^  0t  qok  hoc  diief  mHft^nti  preterrre  nc' 
qnee.  Volonc  ifti  grsTitacCm  oriri  ab  imptiKione  fixA* 
4i  cuftispiftm  fohtiHifimi  tcrram  imdiquc  ftmbicnfiSy 
*  ^od  tpfiim  gravc  non  fit,  lcd  t^tmtti  caa(a  gravitatis^ 
Itque  ia  eo  con(entiunt  omnes«  Circa  vere  fluidi  iU 
lins  naturam,  &  mod«m,  qno  gravhfttem  corporttin 
opcratnr  1  noO  «quc  iibs  cenvenit.  Dabo  CartetranO'' 
nnsi  dognm  eoaceptis  s  PhRofopho  quodarn  Gallo  ver* 
bis,  cajus  nomen  non  repCBio;  iic  illei  Cartefitts  iflud 
n^fiitmti  vortM  nmnid  fubtftff  terram  ambit^  ad  in* 
genttm  althudifmn  Jitfira  ttrn^affurfft*    VQhnmryot'» 


J94  Siiti^Ih  OfmVL 

ux  ilb  ^iarimt  mtt  Qiarif  ffximur  tmm  #  flflP 
imfrfffi  i»  tiradit  ^futuri  f^rgiMirf  Cf  0d  ^tam  *JP* 
r^  fnpeudicuUrHm.  Vorticem  bntie  cmttifieSi  fifeg^ 
in  mtdip  ^bmta  vitrea  cttva  rtf§M  gloftdem  flumhmm^ 
ftue  terram  referms\  relijmm  ^h^ee  fartem  rffleri 
aftta^  qU0t  vorticem  exhibeat ;  fi  enim  ghmtm  vitremm  im 
ariem  agas^  maveiimr  ofua  in  circuiit  a^Xaseri  glaudae 
fOraU^ie ,  C^  ad  efm  axem  perfendicuiarilnttt  bec  «•# 
d^lcit  eamfarati$j  fted^ind^a  byfoAefi  gfmu  flmnii^e 
eadem  vehcitme  aeigatari  maveatur  cum  aqua;  couer^ 
vero  iujyfiewmte  CarteJS  maseria  fukttks  etiam  frefejiim 
ferficiem,  tarree  tj.es  felacim  moveeur  ab  Occideme  nr 
Orientem^  quam  fortet  hfiet  tertet»  Hoc  Jbffefiet  iw 
quit  Cartefim:  muterid  JiAtiist  partes  Itoltut  vim  etttm 
trifuggm  ttttgt  ntaxtmam ,  tfla  nituttmr  recedtre  a  ttu» 
trtfiii  ueotm  ^  ftu  circuU  ^  qHtm  dtjtribetut'^  dtme  ergjt 
fartibus  iUet  mifiettettr  ctrftra  aliqua^  fum  fttittu  eta  ba»^ 
bettt  vim  cttttrifagfmt ,  v.  g»  ttrftra  ttrrtjhna^  .  tta  its 
tireum  ag^mtttr  mutta  Ittttkitf  a  mmtria  UUtJititiU  ptU 
Itmttir*  at  ifudtmtur  adtttttrttttt,  tttu  Himi  aa  dum  oliutttL. 
V  aqua  tir^ulurt  etguutur  iughbt  vkrta^  tleum^  msstt 
minartm  babet  vim  ceutr^fu^mf.  tttttrum  fttte^  ^  fif^, 
titra  gttU  reUttfUie  fmtibue  agme^  Hte  imttiieum(fu^ 
tut  tnvnymn»)  iugttdoJitmfitst^frttfMmOtttif/uttxe' 
jftribue,  at  ueinm  vttum^ 

&M.  JL  Ntitrtaui  Cemewiim  Mu  mitfi!^; 
M  ptiua  rtmmitA  pkccc  <iiicrifiiinii«  tiwi  gmitmem 
imtue  f  &  ftndm  intcrtiedii*  Gnrrscau»  nomiM  «iia^ 
iiihil  snrdt^OyqwfiirflocitatefR  corporit  deC^)dcfiiii^ 
fire  coffmc  liMgnttm  fit^  Seu  ptrvttfli  /  nSiil  igittir  c4 
frcritttcm  ftcit  maSk.  ^  Ponderif  oomiae  renire  debef 
rcioeitce  corpori»  dc&cndlcfitk,  fe4  miiltiptieacc  per  mcC 
fim«      SpcAcri  ciiMli  iolci  veltdsm   fotemiaUe  ,\  jftuu 

SebtL  ttl.  Aihntt  tirefti^^m  tiiqoc»  pnRmttcrf 
htkuu  >  Mai,  ^o4  fcntio^  cspolMfif, 

hCtt* 

0 


Df  mmtu  grMium.  9^% 

L  Cmrfvr^  tm^ria  mnma  vi  gravitatif  firkmu^ 
sd  €tntrum  terra^  9fl  fr»fe  tenmim  i  mm  ferimtiir  vt 
graviratiir  fyi\%i$  Uft«a, perp«n4icttlart  ad  fiiperfieieincefw 
r«  (qiiiKl  tibvia  phcfiomem  obArvencet  tdverrimof  )• 
Eft  vero  figure  tertc  (pbcr^dka  qtitdem  ^  lcd  ctmen 
proxime  ad  i^hxrictm  tccedetity  tit  eltbi  crinritiir* 
Omntt  iifiet  perpendtcnltrtt  td  fnperfictem  ^«rtcam 
nel  prope  Q>hari€tm  fi' conttnfiatt  prodncator,  trenfic. 
^  fcr  ccntrttan  ittiot  fiipcrficici,  aiir  prope  iUnd  i  ergo» 

JL  Oftmh  f^rpora  urrtftria^  {  noHo  dernpto,  non 
1#re,  non  igne)  gravia  fant.  De  oCre,  &  igne  dicam 
locis  propriis»  Die  ^orporabnt  reliqjait  tAnrnti  eCitm- 
one  de  tis,  qusr  vnlgo  levifllmt  habcntur,  ad^  expcricn- 
tiam  provoco.  Eiriffivcro  quld  vo!go  levins  fiiino  f  (ed 
tamen  £  candeb  accenia  in  rccipienre  machins  pncv* 
maticx  conftitoatmr ,  exhanfto  aCre  fltmma  reftiogni* 
tur,  &  fumDt,  qni  prinf  (iiperiorcm  reciptcmit  parteiQ 
'occopavcrat,  mofidrt  in  dtfcnm  mtcbintt  pnevmaticA 
Arqui  ph«nomenon  ilhid  plaiiiffimecommonftratromi 
gravitatcm  ;  neqiie  ettolii  ramnm  (nr  attoltitor  pkronz* 
qne  cxtra  vecoom)  nifi  ob  mtiorem  ttrit  gravttacem; 
ergo*  lo  rtliqttit  corptirtbnty  qiionim  grtvittt  expe« 
rimencis  immedietit  explortri  neyiic,  tb  analogjfi  re« 
petendt  cft  probotio^ 

111«  Omuia  urfra  mrifiria  iu  iiiim  urr^i  Ucif^ 
aH$  m  iaJnm  a  tetmr»  dtfiatma^  mfaali  vilodtatt  ftrmu 
tur  virJM  aiurmni  nrrm  ( (obltco  rcfiffenno  oCrit) ; 
frmuiruMa  ammu  ufudiiir  -fravim  fimt^  Veffcm  bse 
menifefto  fir  ope  eyfindrl  vicrel  oCfe  ttocntti ,  in  qn» 
nrnnmottorenoft  plnmnb  eideto  od  flnfiim  velocftoco 
dofisendmir* 

IV,  Carfarmm  wrmuimgrmukm  uainm  mmifi  4m 
tfvtrfii  urrm  IhS*,  vmriatmt  fru  vmrittatt  kdrmmt^ 
PoficioiMin  kmt  tlitcrtffiNMiy. ft  4«A|iAr fiw,  ^aU 


%i6  Seiiit^  u.  c^put  n. 

0fUA$orf  qtii4  ^if  nrr<t  \$c,  htvnktt  infiAti3t>0S  ax^ 
tmr^  dicttor  linca  itnmobilil)  tircaqaim  tma  gytflf, 
•c  revolvitun  fQli  terntt  dicttntur  g«  ind  ilia  punda 
inperficiei  tcrrcftrii,  qaae  runt  tn  extrc  nitate  mcmora- 
|i  axif  'terrx«  Mquator  terra  nuivcupattir  circnlns  ift 
terra  dcftriptns,  cojus  omnia  periplicrix  punfia  a  fo\i$ 
diftcnt  90.  gradibtts.  Finge  punOum  ftpcrficiei  tcr* 
rcltits  cqualiter  a  polo  utroque  dtftans,  <k  rotationo 
diurna  «bripmm  dum  in  fc  rcdcat  (redit  autem  lapfii 
horis  aj  ,  56',^  4"  ^;  defcribct  pcriphcriam  circtilt 
qui  squator  tcrrx  nominatun  His  pofilis  fic  vcritt 
tcm  priorem  cfFero«  '    *- 

Corpora  tnagU  gravia  funt  Jiib  polis  ternt',  mimi- 
tur  gravhaSy  prout  a  fotis  receduur  ad  aqtiatorem  ;  ;/;/* 
iiima  omniUin  eft  gravttas  fub  aquatore.  •  Id  cxpcrtits 
cft  Kicherus  in  Infula  Cayenna  fiib  latitudine  Auftrali 
quinquc  cifcitcr  griduum,  h.  c.  fci^e  ^fub  «quatofe  fitJl. 
Adycrtit  illc  pcndulnm  idcm,  quod  Parijiu  fccum  do- 
vTcxcrat,  lcntius  ofcillare,  quam  Parifils,  duobus  fcre  ml- 
nutis,  &  i^t^  MaupertUiJiUfft  rccitat  1*.  Mako^  qui  opff 
inftnimeriti  a  cclcberrimo  Grahaino  cum  iii  fincm  pe* 
citliari  artificiq  elaborati  hotavif  Felti  in  Laponia  fub 
Iatitudine66^j  &48',  tcmpore  unius  rcvoltilionis  fixa- 
fura  ,  ofcillatioiies  864^3.  '  Parifiis  autem,  ubi  latitudj 
cft  48^,50'  ofcillationcs  86395,  feli  J8-  pauciores;  lo- 
cos  autem  obfervationibus  faciendis  aptatu^  fic  otro- 
qtic  artemperabattii',  ut  idem  omnino  effct  calofis  gra- 
dos,  quod  thermomctri  opa  diligenter  cxploratum  cft# 

Idcffl  lfiud\iotarunt  Aeadcmiei  €a]li  a  Ludtviai 
XV.  tcmponbos  proximc  lapfis  miifi ,  ut  grados  tcr- 
rcftris  meniuram  prope  aquoiorem  cxplorcnt  ttfai  pcn^^ 
dulum  lentius  o(cillavi(fe  compertum  cft;  cx  oppo^ 
fito ,  qui  ad  ptagam  feptentrionalem  abierunt ,  gradum 
terfeftrt|Qn  poloi^quam  fieri  poflct,  viciniiSmttm  cxami* 
ncturi,  deprchcnderunt  idcm  pcndolum  iub  circnlopd* 
lart  ctfttliarc  c^ios)  qmm  Parifiis.     Diat   ordllatii^- 

^  num 


/ 


Hft  motu  grivium.  i^^f 

fiQm  VartetiS  pendet  d  Yiria.V^locifate,  qut  fendalr 
rerlus  cencrum  tec^rc  teruntnr.     Quare  minor  eft  relo*. 
cit^s  Cayemia  f  qoam  Parifin ;  minor  fari//4r,  qutai 
iVfii;  mtnor  /?/*  ^uatore  ^  -  qvLzm  Jhb  drcuh  poiarh. 
Velocitas/  qua  cdrpdra  feruntor  verias  centrum,  grdt^ 
f<v/eft  (  ScboL  frac,^  ;  grayitas  ergo  mininria  eft  fub^ 
iEquatorc^ ;  .fitque  (emper  eo  major,  quo  corpua  magif 
recedit  A  iEijnatore  ad  pobs ;  hlnc  ii  idem  bmnino 
corpas  deioco  alio  in  aliom  transferetur,gravita<cm  di«' 
VeirCim  obtincre  potplE       Jam  gravitas  augebi^ur,  jSf 
fiTrpus  viciaius  fiet  f^olo  terr^ ;  jam  minuetuT;  (i  remOf| 
tins  ;    eft  enim  teita  ad  polo|  complanata^  ad^qud^' 
forem  protuberans  ^j^juare  minus  diltat  gravc  a  cenfrit^ 
tm«  fub  polis :  'magiS  fob  /Eqoatore*  *  ^ 

'  His  qtiidem  bblijrvationibui^  nititur  affertfo ;  fct 
obfervationum ,  8c  experirnentorum  ratio  danda  e&i 
Sic  exiftimo  :  Omm  fuperficiei  tetrefiri$  farus  cin^ 
4xem  terra  revoluta  bdhettt  viret  centrtfug^ ;  ali^  m$^ 
j%res  y  tnimres  alia  ,  prout  ad  ^qdatorem  propius  it* 
ceflerint^  aut  ab  eo  longtus  receflerint ;  ofmium  maxi^' 
liias  habeht  corpord  fub  JEquaton  pofittk»  AiTertionit 
fi^jns  veriiatem,  ^c  ^niiim  uberlus  iexponam  admotuia 
in  lifieis' cnrvis ;  interea  nocafle  fufiiciat :  terraoi  fingtt^ 
lls~diebtis  eirca  axem  fuum  converti^  ac  proinde  fiaguii 
laa(uperficiei.terreftri«  partea  <  figeminaejns  pundt^ 
^los  inqnam-fi  excipias  )  qnot  di ebns  circnlum  defcri^. 
fcere;  Atqui^corpus  omne  circulum  deCbribenf  gaudetf 
i^i^jis  laentrifugis  a  aiotn  tangentiaU  orris,  ut  ex  infr» 
dkendis  patebix  ;  ergo.  Vis  iila  ccntrifuga  confiderari 
^eft  ut  contiraria  gravitati «  &  veint  de  ea  aliquid  df*^ 
cerpens;  bincquo  major  eft  vis  centrifuga  ^  faoc  aini*' 
]itias  detrahere  videtur  dc  gravitateV  Quantitas  asiteq||, 
vis^ceptprifugpB  pendet  {  caeteris  paribus  )  %  veiocitatfli 

Srationis;;  atqui  major  cft  veiocltas  gyr;itloatP: 
JEqiiatore%»  ,  quam  propa  foUs  (  codein  cniiii^ 
temjpovc  niajora  (patia  ,  id  cft  tnaiores  circulos  cpa« 
VlSmt  cb/g^tii  iU  Mftamm  pbfita,  qiaam  #tf  pjb 


tfsi  nbi  rtro  tvfit,   habetor  Ct  t^  St  i    ^.  ff%, 

SfboL  IV»  )  prouuic  majorcin  e^c  oportcc  viin  ccntrU 
fugamyif^  Mquaun^  qttam  prope  polos.  Hm  una  cft 
pbxnoinchi  ratio^  cx.qua  cadcin  dcdoet  lolct  terraoi 
non  cxacke  iphatricam.cflci  fcd  fphstroidicaiti,  cd  ^los 
lcilicct  coaiplanataoii  fub  iEquitpro  protubinmtcai^ 

Jaoi  quscritui'  i  quomodo  eo^pdrc  (ob  XqUatdi^i^ 
l^ofita  adhuc  ih  tcrram  rccidaiit^  cnm  oiiticn  corundcnt 
Vjs  cciitrifuga  propter  matimam  fotationic  cclerititcnl 
cflc  ciebeat  iongc  maxima  f  l^*.  quk  gravitiS  corpc^ 
rnm'  abunde  iiifHcit  ad  irim  iilf  m  nbiquc  cocrccndain  ^ 
^tianivia  cam  <*oitf!ccere  itcquit  fiiic  dii<|ua^  &  vi  «fcmfrifur, 
gat  ptoportionata  (ui  dimlnutiorii ;  tft  ncmpc  ( US^ 
MoskovUbio^)  vis  cf ntrifnga  (iib  ^q^tort  td  yim  gni> 
VKatis^  ut  i :  ad  989«  Quod  nc  dixiuc  (olum  videttoi^^ 
lic  commonftrat  i  Sit  in  figo^  tt.  oxcmi,Mk  is^  qui  uno 
iecundo  horario  perCiirritur  Cvh  jfequatort  |  qui  tft  tk^ 
cuiidorum  1 5«  Erit  CB  (  /cmidiafnetcr  iEquatorj|| 
^ux  tx  BofigUefh  cft  pcdom  Pari(ieri<ium  t^i^iiiH  | 
miDiy  ut  radi^s  looooooodoooo  nA  (inum  vcrnint 
^cundorum  1 5  ,  quat  uno  fccund^  tcitipQris  l^rcui^« 

rumur,  fivt  ad  1^44  ;  ntfide  proVenintit  tiiieit  f»  i-^~4 

1006 
£ft  autemf  ititervallum  it  (quod  obiervatof  in  gravibtti 
llberc'  defcendenttbus  vi  grivitatis  urio  fccandoi  }  ffi* 

jluifi  Ij,  lin.  7.  — -  j  igitnt  crit  tif  cenltrify|^il  «4: 

160 

vrm  gravitatis  tvt  T:  ifd  sSs^*  $ie  d^oeet  ^ctcrmtndii^ 
dam  cfTe  reltfrioncfn  vit  (fenttifuga;  ^d  vim  grayitatii 
iiib  iEquatore^  .        . 

Interea  tameh  rtoii  ncgaveriife  fieri  poile.  iit,  n  tnlf»' 
j6r  etret  vis  centrifuga  fub  ^quatorc,  fivc,  <|u6d  cMciil 

secidit^  fi  ttrri  gjxatti  ttitrisf ,  ^vuatn  ^li  l^i  4»  ^^ 


j 


pfsftik  t^b  ifiqti«tore  nofi  «mpliiis  dfoit  -gtivtii  r;  p^tDs^ 
tnim  €(rc  celeritas  tevolutioiiHS  Itma .»  ut  omnein  (Ub 
iteqdhtort  glravitatem  {>crimer€t.  Scrutcmur ,  quaii* 
tam  eJiIe  cpoi^teret  velocitattfm  illtfm;;  facllias  iude.pato- 
iiit^  qQanta  pars  grafvitatts  fub  i£qoatore  Wimatur  .pec 
li^^ditidoneAi  terr^  diurniifn  iciroa  tttem  twm,. 

•^  «it  cfwulus  BtD  (fig."i>.)  rept^firitaitsiE^lit!.* 
torem  terr^  gyrantem  »b  Ooiridenre  '2n  'Orieritettv 
Defigjiet  LM  15.  pedes  ri^ios,  quos  eoj^pus  L  ^edorrit 
lAi*  ftcofndo  hotario,  ditm  Vcrltls  H:enf rOm  ■  terr« 'fcr.*. 
•  Mr  f»  griatittftem  Vi  centrifogir  noh  imhiinutflm. 
£x  pufnao  M  e!figifur^pendttiflCrls'il!fJS,  doniec*^c« 
tcorrat  :peripheris  in  B;  tvtm  ex  JLditcitUr  parallebi 
£i^r^ttnipfietoque  parafieiogrtmino  Af>^  neinondti 
Smdlfg^  i  't  corpore  L  g^fm^inis  ¥ti*]bits;fmpal(b  &« 
gimd^ta  dii^aiefnes  LA,  &  I/M  deferibendatm  efle  diit** 
^gonikltm  LB^  ^qtio  cafu  edatnfi  «orpiis  Lndn  qtiiefcati, 
mPD^n^  cum  f  j>unSo  L  rrftitsfei^f  hr  in  '£,  nequfcaicietK 
^um  terrflt  accedit,  nec  ab  eodem^recedit;  proindequ^ 
Ihm:  ^Iq  ^rftvitKS  f  rope  omriis  adffnrj^ta  ^effc  ccnfetue^ 
iper  Vrmeenritfifgim  ele  gyracione  ortam.  ^ameOTeil 
tets  'rectdky  fit  Wlor  diagdmiilrs  LB  f\tt  "e^l^loretur  ;r 
lioc  cognito  fimoi  veiockas  Inndtefcet)  e  qua  'nafci  diBk 
lll^at  ttnia  «'is  trentrifuga  ,  Ut  'oitinem  fub  ^qtiatoir^ 
grtvitatem  tdimerc  \i2eatur.  Ifiad  ope  MGfec^tnetrii^ 
jprioGO  i  , 

^liim  i.BD  rOiiixi^Am  efl:  >*  etiin  enimHiiigir* 
his.  lOmnts  td  peripfaertSK  pQn£ltf<n  "«Hqiiod  terminttto^ 
^  ^ioickcuto^  iive  dianfetit)  tniifteits  -redus  ^ » 'etiat^ 
iriRg^las  ad  B  redus  erit;  ex  coius  verttce  fi  In  liypo* 
llif^oftfn  demittatur  perpc^dicnlayis,  dividet  hirc  dir- 
lo^  t^ikxxk  ih  duo  tliii ,  taofi  fibt^  qukm  toti  SMlik 
rutruffi^ufe  pcr  Gcoto. )  \  quirc  /^lufti  UBD  co  A1# 
XSU^  bbf ihebitque  bsc  j^ropbrtib :  Lt> :  IS  si:  hBi 

iM^  tt^MiiA^iAt^Lbthiki  «(l^s:  Y 


M  S$Bh  Tt.  Cifwt  VI 


XD  m  LM.  AfTQmartir  ireriiin  ex  B^upari^  LD  isi 
%^6%  1717)  pcd-  ParificnCam  ;  &  LAt  ?;  1 )  ped  ?  fict 

tBsA  Y  19*817171  ><,  «5  =!  fi^"  54JJ4-  Qnarefi 
celcriru  rotarionis  tanra  cfTcr ,  ur  corpof  fub  Aqoarore 
pofiram  dccarrcrcr  moro  communi  com  rerra  54314«. 
pcdct ,  iftud  ncqoe  ad  cenrrom  rcrrs  acccdcrcr ,  ncque 
ib  co  reccdcrer^ficqae  perempta  bdmcrar  omois  prof  e* 
itiodam  gravitai* 

Adhac  vidcn(lam ,  quot  pedcs  corpos  Cvlb  Mqn^ 
tore  hodie  pcrcurrar,,  mora  lcilicet  communi  rcrriginiiL  ^      -  j 
&  in  (ydcmare,  i^  terra  cirea  axcm  room  conyecti      ^  ' 

dicirar  tntra  sf. ,  f6*  •  4.  Sieargoos  aflTuflit»  4f|Hneirf 
refpondcre  dcbct  per ipheria  ferc  6 1 800591 )  pcd*  (  qoe^ 
ruu  raiio.prope  eadem  eft  td  diimetromi  qo«  SI4  «4 

100  ) ;  ergo  fi  corpui  fiib  JEqaarore  pofitom  imii  t}»^ 

56,  4  s  86164  decurrit  61800592;  ped/;  ooceffif 
oft  unp  (ccundo  horario  decurrat  7171*  pcd.^  qfii;mi#*  ^ 
mcrui  prope  (cpries  miaor  cA  eo  pedam  nameroi  qoot 

jotra  1.  conficcre  dcberet,  (t  omnis  corporom  gravkf^ 
fnb  A)quarorc  exfHnguenda  Qffist ;  ergo  fi  tcrra  (cprr^ 
celcriui  circa  axcm  iuum  con^ercrctury  h.  e  fi  revoki' 
.  tioncm  fuam  intra  horas  trcs,  flt^vigititi  aliquot  itiinato 
abroivercr,  jam  omm's  corporum  graviras  rubJata  tiff^t 
fique  velociui  adhoe  gyraret,  jam  partcs  iSqaatorii*  teiv 
ceol  diflSparentur*  *        ^ 


V.  Corpora  terrt/lria  in  vdriHf  «  antro  ume  JSU 
fiantiif^  fid  adniodum  mapiif^  variam  babtHt  grainia^ 
sem  ^  fivc  j  itquali  velocitate  uon  feruntur  vtrfiu  ctn* 
srum  temt.  Pofitiohx^-floitex.pfibcc;  cprpor a  c|^K!!% 
miuttsgraviati^uiabsSlfyatore^  ^aamadpolol;  arqoT 


cor< 


Mrpofi  «4  fN»Iot  eonftitnta  fiine  cenM  tcnrc  ?icini9*' 
ri»  Ab  JE<]u«rbre  (a  it  tb  eodem  remoriora  f  (tipponn 
cnim  boe  loco  :  cerram  «d  poloi  compUnaum  ^  (ab 
JEqa8'tore  proeufacrantem,  quod  alibi  ex  diverni  graUi» 
Voa  Nferidiani  maniftfle  evincam  } ;  argo. 

Qaanqoam  licet  quiefcere  ponacor  terra»  a«c 
<6garam  exaSe  fpbsricam  obtlnere,  adhoc  ilU  gravic4« 
tom  varieras  locum  habere  poteft.  Jd  ut  appareat^ 
CcTibk?.Maki^Jedttlo  advertetidumeflyCirca  £quatorem 
$trrd  miuut  adeffi  materide,  quam  circa  polos^  idque  duplld 
ax  capitet  Pnmum^  quiafiih  jEquatore  propter  ialoru  ptr^ 
^fituos^  quibut  metaUa  ipfit  ttqn  ttibil  didttcuutur^  omuia  cofm 
fora^rariora /ittity  quam adpolos^uhi  coutiitua  bjeths^if 
glacies  ctt»8a  adflritigit ,  (9  f  H  arSum  cojpt*  Deitida 
quia  fftulto  minor  eft  deujttat  marium,  quaftt  terret  ^  /4k 
pidtMt,  metaUorum  ^  e  quibtu  coutitietis  coagmentatttr  i 
fter^que  autem  ohfervatiouis  iu  America  fitut  iuftituta  ^ 
isiqua  tttaritimit  lods^quore  vafiiffimo  circutnfufis^  ^HJ^ 
(^  ejtplicatia  magua  eft  ^  &  profutiditM  ingetit.  E/t 
prttterea  non  parum  verijitnile,  eaverttat  iUic  iueffefubm 
ierraneat  £f  crehrae^  &  maguat^  ut  indicautfrequetttilpm 
mi  terr^  motut,  His  pofitis  raciociniom  (uum  conficit 
laudatus  Audor  Inftic.  Phyfi&P*  I.  Sed.  IV.  c,  II.  ^ 
iig.  Schol. ,  qood  yideator »  non  tamen  prioSi  quam 
r.e£te  tQtelledis  attraaionom,  &  gravitatom  legtbua, 
ooaa  infra  ir«oicabo% 

VI.  yaria  corporum  gravltat  ita  pendet  a  vttri^^ 
difiatitiis^  ut  eadem  feqnatur  rationem  reciprocam  dupU* 
wam  diftantiarum  u  centro  urr^t ;  i#  e.  (t  corpus  A 
duplo.magis  diftet  acentro  cerrci  quam  corpos  B^ 
crit  gravitas  corporis  A  ad  iUatn  corporis  B ,  oc 
s#  ad  4*  t^ am  gravitas ,  tftm  eorpora  terrcftria  orgat 
Tcrrus  centrom  cerrae ,  eadem  poto  eft  com  vi  cenrrali  ^^ 
^%  Lonam  retinet.  in  orbita  (ua  elliptieai  in  qoa  cir* 
cora  terram  revolvitor  :  ellipiia  aotem  deferiKi  neqoic^ 
10  pomcar  v|^  cemripeta  uqoi  rt|ioneai  rcciproceiii 


jpiiptieftt«ii|..  fliftantiarutn.  a  f6<H>.;   eicgo.     Nfinor-tkH^ 
4«  jpcoi^abitoi:  CK  iif ^  qdat  ^.  nipfiiif^;  i.tv  lii^eis  ciifvi|ii: 

<Oit|(>ar.atioiic  fpi» tij,  quofl  L^fia,  con^^jt  npg,  p/^f^ 
l^oraf tp,  rerrus;  tcrrani  cadei^dp,  (i  {qli  vi  (^cntf  iyct»  ce« 
Kpquerctuf: ,  &  alfccin^.  ipatii',  quoA  ^Mm  ^PPW^^ 
Corpoca..  tcrycftriak  dccurrmit,  <;a4cu4o.  ncr%  ccjov.cwoi 


ttin#Jgini«.  (:qup4nau!o.n|pxpi^VPjq»,d8^^^^ 
ij'  pcrmitterf  tujr> a£^tptii,  tcn« ,  u^p  prJmp^ hprarip  v;ci>. 
^pf^teriiBm.  ca4ci|i^^C|^c,qrreret  1 5-  pecjcs  v  cupi  cx  atfcj.  i 

vcrfii. corporai, tcrreftria  (' qup^i  expcriiisntiis  benc  mujti •• 
i(onipcpt4imvhabe(ni)?)  up6,y>ctt/fii?.  verfi»  rer^^^caL^ 
^jpndo.  ctiam.  dtcurrant  pedcs  1%*;  quarC;  ttn^j^ote  fik, 
^agies  bipeWori;  totidcm,  ped^ss  c6n(iciutu>  qupt  Lt|09< 
$ci^Qnp,minpto,^rfi»^  qqot,  taijdicm,conficl'ent  ?^' '  Ajj^v^ 
54000 ;  n^m  cprpora,  i|i  ccntrupi,  Cbs)n},  debb^ntia^  v^ 
fpravitatiSr  dclabuntur  ;^  cft  v.qro  gravitas  V*  ^ccejiirafri^ii 
^nfiat^f  qasi.poRtitcreCciifit  (pani  CDtaha,  ut  quddrat4 
^mporiini.  (  it*,ncm^pe  habct  tI}Corit  (jf///^i  expQfit^ 
f.  i6d. >;  crgoii^corppra  tcrreftiduinnoj^rir^d  dccur- 
i^nt  pedcs  x,^:  i  6p.fec^ndif,  fiv;e  unp^iwif  54P00.  pcd,' 
dccarrcoN     Porro  cuif!  fit  c$.dcn?  rajio  15.  gd  54000«^ 
^0«    I.    ad''  ^600,  c^riifima    cpn(c.CQtjpne;  clicitat  i 
^crfm.  in  Jnperfieie^urM^  attt^prope  eam  pofituin  tef< 
miUtes,  fixeenties.  majut  Jjuitium  cmfieer^  caienio  wi^^ 
^ntrum  terr^  ^  quMmLpna  c^nj[edurajjfft^^  pe.rjiiiu^ 
Metur  vi  folinSsgravitatis  iti  ter.ram  5  promde  gravitatj;^ 
t0rpjorum,terrefinutn.  ejfe  ad  gravitatem  Lufke^  ttt  3600.,. ' 
#rf  i.^      A^^ii  h^c^cadcm  cft  ratio  r^c5||roc^ 'dupliqatai, 
diftantiaram  a  ccntiK).  t^rr^ ;  d^ftar  ehlin,  Lun%  a  tcrra'        | 
9000O/  Ipucas ,'    five  ,    cuin  raditis  tcrrcfti;i^  adatqoct. 
Y500.  lcQcas ,  crit  diftanti^  tuns  ^^  ftu  radhjt  orbita^ 
.  Idinaris  ^:^  60  radii^,  tcrrcftribu^ ;  quarc  diftaiitia  cor- 
paris  ia  fuperficii^  ^«rrar  pojjti  a,.^c;itrp  terr«  cft  tci^ 
cUft^kant  Lmx  ab  eod.em  c^mrp,  ut  r.  ad  60;,  quo-. 
ffnm  q^i»drata  Ihns  i.  '6c  1600, ,     Solicitc  aottrt  in«*  ' 
rcQtiir^  q^  m  bnnc  feVani  congcffi.  Sc4 


0»  Mof M  ffrMhim,  *ii 

'   ■   SM  en!«n  ^eggerit  nonneme  t  qnit  «ed«t  Wfr 

«am ,  (i  fobko  priwctnr  moH»  fuo  projcaiii,  &  pe^. 

pifc«retnr  foli  •aioni  vis  ceniripct« ,  uno  mipoto  cr«. 

H»  q^}nde«im  onanino  pedes  «fle  confcaoram  ?  Cr^ 
^ci,  fpondco,  quuquis  ad  fcquentU  animum  advertet^ 
$t  i,5  arcti»  1«  U\v>M  d«fCTipti«  wo  horariQ  prtm» 
i  fig.  pr«a  )  qol  defcribitur  «mini|  viribot ,  alter» 
trcjtm  ftcunduTO  tangentem  *..^,  «Itera  centrah  ^ 
cundum  direaipa<m  ^M ;  exprimit  autem  lineaLA^ 
per  quantum  ({«athimvis  ccntralU  tempore  unntf  frimt 
borarii  defleacre  facUtLunam  a  tan§cnte  fua  pcreor, 

«irenda  ,  fi  y{$  ceotralia  abeff^t  \  ac  p^oinde  qoanturn 
Una  fpatiom  decorrcret  cadcndo  ijerfu»  t^rrani  ,  ^ 
tbcffet  vU  projeailis.     Atqui  ?»"«  t,»^»'".'»!'*  f f* 

Jognofci  ;  cu«.  onim  A««  i«P  .  &  f  ^?n*""f  « 
|h)t,  ot  fumnpkoimi,  hafeeWwf  fto^otofi  i4l«  *« 

W  tBt  LMy  fpmlM^  — .    QMath«t«  ^*. 

&  m  co«ilt«  fonr }  ID  «uldem  eft  diameteiE  «Atnm 
lonarU,  «qoe  «deo  diK>la  radii  j  £B  arcui  eft  •  Lun* 
nao  frmm^  homio  defcrifto»,  eojui  valoeem  hc«  wve. 

nirc  •rgDcnd»  I  Lnnaintr»»?,  7.  Jt'**''»^''*  ~*!?" 
Bcriptieriam ;  nno  prime  minuto  qnamum  arcom  *> 
oirret?    HU,  ui.quam,cogn>tU  innotef^tLM.    Kcn» 

in  nu«n«rii  ^jeiUwr  tytAV  ««"»?«'»»  *•'**  ^  *** 
|od, 

Qoemaamodn»  dM*  dUmewo  invenUtur  perfc 
plioriar  docet  MatheB».  Si  taroen  unul  aliqut»  opcrv 
Cionnm  Arithmeriearem  tmparieni  eflet,  ftqueme  coni. 
pendio  wi  yoterU:  ex  r^c««iffimU  ©allorum  obl«r- 
V«Hon%at  in  eompcRO,  habemni  \  ctrculum  tcer*  nio. 
Stimom  compleai  i»f»49<oo.  ped.FariC,  qni  nume- 

flu  11«  it  iwilci^iaaw  dabit  pnrii^ian.t»*"*  uir 

^'  K4      ^         -  ««*% 


*  ' 


$6j  Se^ioll  Cdfuin^ 

l»trit  f  cnjttf  ftivai  eiioi  pxap§s  fotfjof  %t  ndio  Hg^ 
reftrif  eriam  peripheriain  orbirs  LaDarii  fexagies  inajo» 
rtm  efTe  oportec  peripheria  circQii  miximi  cerreftris  f 
iemper  enim  £  :  r  s:  f  :^  ,  five:  loos  loo  s?  3X4« 
$14« 

Oggtritur  ienu^  EfieftQf  gra?itatit  Lantns  noii 
Omnino    confenriunt    effe^Ubuf  graviratfi   terreftlns  i 
lltdenus  enim  in  motus  Lanaris  &  rerreftriji  inreftigt» 
^one ,  ac  conrentione  rcperta  non  eft  extdi(Hma  rario 
inverfii  doplicatarum  diftannaram  ;  ergo  f]|  illt  ,  qom 
(unt  vtrfus  centrum  terrz  urgetur ,  non  etdem  eft» 
cam  vi  gravitatis  corpomm  terre(iriam«     '^m  non  di£» 
fiteor,  rarionem  illtm  td  fummum  Geometriear  a^qmiTs 
Iitatis  rigorem  haud  exaftam  efle  ;  in  cauflt  eft ,  quod 
Iruna  in  orbita  fua  noi^  moveatur  ri  tott  gravirttis  in 
terram,  (ed  aiiqut  Gx\  ptrte  mnlttffa  per  tfiionem  Sor»; 
tum  quod  neque  circt  eentrum  telluris  movetrury  (ed 
mct  eommune  ntrinsqoe  grtvttatii  ceatrimi ,  qo<^  tx^ 
tft  cenrrum  terr^  po%im  eft<   Addunr  afii :  quodLunt 
non  feratur  in  orbitt  circulari,  (ed  elfiptictf  qaamvif 
parom  iftt  abiit  t  circulari.  Hitc  omhia^  tit  BodLoviehfaf,*^ 
itbuiffent  diligemer  confiderare  u&rmuU$ ,  qui .  Neutmtm^ 
aarpunt  idcirco  ,  qmi  nou  penitus  accuratijjiptam  tnve» 
niant  ratiomm  quadrati  diflanuarum  hti  effk&u  graivtus* 
Hs  terreJtriSj  &  LuMris. 

,  Rurfum  ohjicimri  Ob(ervtvit  CL  Mufchentrakitss  i 
grtvitatis  effe£):us  terreftres  mutuo  comptratos  non  (t* 
tis  exadc  refpondere  ratipni  inverfae  daplicatse  diftan- 
titruro.  Idem  i(lud  citmant  plerique  omnes  Libri  td 
materiam  de  gravjtate  confcripti;  ergp.  ly.  cum  ci-  - 
tato  AuSore  :  ftac  aierrado.  a  iege  rnverfa  quadrato^ 
rum  diflantite  potuit  o*:iri  tum  a  pgura  terr^  fpbanfi' 
ia0f  parsim  ab  ohferpationilus  minus  accuratit  ^  parttMta 
qptia  raitui  terra  uanium,faris  tfens  iefirtmuatus  efl, 
mt  fuUpss^ss  fsrriS  tffiii  itfl  hme^emrfyi  Vnc  inia 


UUi9K^Mf,fr9ptir  muItMf  vujgMffminkmi  levimt^ 
\f  fVTPfior^  $4  probamibm  cnSris  terra  tnHtbut^  f^ 
mflra  ^tat9  iu  uuivtrfi  terramm  arie  eomigenm^ 
T^eu^mu  non  abfimilem  ohyt&iomm  fic  diloic  L»  f« 
princip.  prop;  ^ma  :  Si  fuif  pbjiciof^  fuod  mrporq  a^ 
uiaj  qu4t  apui  ms  fuut  ^  bac'kge  gravitare  debertut  v$ 
fe  mutuo ,  cum  tamen  eftumodi  gravitm  nuuquant  fiiu 
tiatur  ;  refioudeo ,  fuod  gravit^  i»  bac  corfiora^  cum 
j/Sr  adgrapitaiem  in  terrqm.  tkeam^  Uf  fitn$  bac  corp^ 
ra  ad  ierram  totam^  lotige  mimr  efi  ^  ftam  ftkt  fith 
iiri  fojpt.  ^ 

Deuijtte  :  Si  varia  Ct  eorpontm  g^itaslR  v«ril| 

«  eentro  terrx  difiantttt^red  admodnm  magoai»opOTt«btt 

incrementnm  gravitatis  verfiia  poto$  eflc»  ut  qaadrai^ 

tpm  finof  latitpdintf  ,  qn^d  demottftratoip  dcderoQf 

Nemouut^  Boskovicbiuf  »  ^  ex  iSts  aKi ;  fatltt  cockfe» 

qoens;  igit^r  &  anrecdena.    Jf.  tmo.  N.  A.  licet  itH 

q^ementum  gravitatit  rttfoa  poloe  non  f^ret  it|  did« 

ratione/adlioc  tamen  i(to  gpr»vita(is  varietts  iiali^i  po(^ 

fcu     9«  adot  DemonlNtiiQi  id  eft  ex  hypoch^fi »  (i 

terra  fit  elliptois  ad  polos  compreQa ,   iteniqoe  fi  ii^ 

iisdem  a  centr<»  diAanttis  fit  homogene^  C  fine  ifi% 

hypothefi  N.    Telturis  figiira  nondum  fitfis  ad  ooincin, 

amuflBoi  determinata  eft;^led  neque  de  ^nCfkiUA  tellii^ 

f  ^  komogencitate  «qoidqu^  certi  habctiirt 

VII.    Corpprum  gravitat  ad  fif^fim  e$iim  ej^  it^ 
iiflamiu  iUiSy  itt  quibm  ^tJgo  experimema  eoffm^  ; 
fiye:  cottflfmsy  ae  u^ifirmie  eft  gravitas  corpmrtMt  iu  di* 
fiamiie  mimribm.      N/im  ftttuoref  illc  difl»OU«  ,  ut- 
cunque  vaijsti  evaneiamt,  ac  prppeoiQdom  9ull«  fiint^ 
fi.cum  radiq  tcrreifari,  qni  4000000  paflc|Ui|i  cpi|ipk». 
&itur  ( paffi^s  aqtem  fingtili  continent  pe4cs  quinque  ) 
CQmponantulr.     Pinse  gravi^stis  experiounntuvi  .sliu4i 
fi^ri  in  part^  ftdificii  in^s^  aliud  in  fitprema »  aliud  iiit^ 
tu|9i  Z4»a(U«cgj&  trKfi»^  idta;  qusQliVr 

Ki  .^        fauii 


A 


..-    ^  A. 


f  4|        $tah  k;  (s^ 


Iplir^pe  dolimiirtipa  ^fifbtm^n,  fi  c^,V«^'ieiteft^ 
Cpnfcrtntar?  Ad  {cnfam  iinlhim  ^m  ;  poterit  prptn^ 
dit inmimr^a^  Aithmih czAcm  tfft  corpoi^am  gr'avit«|; 
f4  («nfuo^ ;  i^ne  optii  dcyiceps  foeric  in  krrra£Honi^ 
l^m .  de  rartone  reciprpca  doj>kc|u  di^nti^i^ruiiii  fi^ 
Vfriore  9en(ya  idyertere^y 

Si|tis  indi^  patet  t  prforet  geirH^aS:  aflfertiqooi  ^ 
Vtftm,&  Vham  iion  ad^difhntias  qQasconque  pertine«i 
M|  ied  admpdam  magnas ,  non  adbca  hBmijifii^ra,  C^ 
^ditior^l ;  hinc  nulla  comparec  graviraris  diverfitaSg 
feo  in  v^iiuis^  iive  in  montibi^s  i^^y^nf ,  eandein  e^^perialf 
Ae*  AK  ii»  montem  KchinM  756.  hexapedas  altom  \^ 
•bi  i^  cipifli-flominis  Amqzonfnn  in  vicom  Para  ,  t^iiiii, 
Sft  orfeefii  Quit0  aftehde  ;  abi  in  yafUfli^nin  itlum. 
^ontem  &imiorseo  i  6c  pfciliiripnum  ,  proindequ^ 
^tis  mictiifra  prqcol  omni  4pbip  iciverte^ 


VIIK.  Corfr^  ijfitJm9olumink^Jid.u9p  episdem 
ienfitath^  e»  ea^etifihahit^dmt  ietalmiria  imequali  ve», 
hcitata  fettmtu»  uerfits  terram  m  media^  rej^ente  i^ 
(Xim  eiugi  fiiciitus  yincttur  iifipeditio  mcdir  i^malfii, 
denfiore^  ^^A  r*ripre,  fierl  plan^  deberi  nt  n?ajpr  fit 
^leriray  corppris  deniipria^  qiiam  larioris,  Pr^  ido  : 
Sir  maA  A^z:  6;  naalGi  5=:  3, ;  ittrtnsque  ceierita& 
^  4.  Erit  qrHmtiras  moruc  m  A^a  94 ;  ih  B^ ^  i  v 
JBqqilibus  msnarom  yf,  &  £  volominibus  refpondere 
^tet  «quilfs  .medii  c/osdein  reflftentic  ;  sqoalia  rejSr. 
ilentia  cqoalem  motus  portfonem  al»  otraque  malfii, 
^  dhecerpir.  Poiuun  decerpi  ur  6-;  bil>ebirup  reudiui  ino*. 
tos  qointifis  iii  miffii  j4-  r:  tf ;  in  Ji'  s:  6*  ^^55^ 
nutem,  per  iilin^  medii..  impeditionein  de  miiBs  pertiC 
le  omninonihii;  periir  ergo  de  cekririre  ;.  irpri>iix^ 
develocircSi  fiiperiri  medii  reiiftentii^erit  in^sa  fi^ 
jil£  =:  1  <nim  6»lisi  S8,  <Sc  s  xsl  =:  f )  qu«  ce». 
Iffrirarom  tncqailiris  eA  pro  nitione  miflinim';  tnu» 
jor  cckricii  t ofpondct  mijori  tmSm  |  SMIlorl  minoi^ 
Hftc  ikpinc  flMUcm^  rcflcAot  Ifmam 


* « 


\  ' 


,&lHfUl^fif/e^r^^  Vaam 

fc(4o«  fi*qni(experimiDniadve?(vtm  hfOiQ  «firupiiem 
|iiigi>ar«  viiJkflQytur  >  ^  w  noo  accarciioiiV^  oevixiiiit 
pQji^^tUefli^i,  aut  fin^  exquijlita  iaftruinemMnni  appaj^fv 
<u>  quo  t^i9.pojrisi  meuibri.  «s^Qe  iQ^tun,  aujideasqjD^ 
jtoa&rt^a;^  diCi^ria}^  pei^exiguiui^  (o\fk.  C^lera  inicif 
f  x^eirimeata  ptobatiffiiaum  faai>etu^  iiiud  htfi^tdwit 
^€9^  vejki9m  JjkiUntni  iiklbrinam  (phars  eiVsf  exficcj^ 
i^ain^  lum  ^iftea  fib^ram  ii^tacimn^  dc  «kM^mi  ipSHfL 

A flfef lioxieB.  iftflA  een.  |^ciinbnla»  tQtUkm  obAvr 
tationes  adferre  placui|.  ^JNin»  a<^  ex]^osiendani  tJev^' 
leiii.  dofiNrinian  «ggredior.  Revocabo  atftena.  ad  gemiv 
pas.  pojuiniiiu^i  profofitiQnec,  quidquiA  ilk  lA  ^f<,^ 

%0ipr4^iu  /um  vi  nftf^^ffinfa  a^mu  in  rjmMfu  rici^ 
jpr^4  dufUeau  diflaf$l,iarum^^  Intelljgo  ^uem 
^ctr^ftronis  niominQ  fiUh  (^etertufbatronem^ 
^uzm  bjabent  cojppora  ^  ut  a(}  (e  ft  aecQdanr^ 
Tcl  ccndan^  certa  tege ,  <^axcQnque  deterix)^ 
«ation^  hujiis  qaufla  fit.  ProU^  Pajr^l^  JSit^ 
vis  corparoi,  tafalia  prddits  funi  ^r  aMi:^4^4,, 
Vlim  iot^t  totafia  nabetBV  Sot ,  tpio  j^^neta^ 
primant»  &;  (eqondsiri^  ^ttnik^,  m^tn  pru» 
mMi  &/  «wiitf  r0y]^4i  pkmi4ff:U^  qued  fio; 
CYinco  >  ^irqa  Sohtm,  lanquan]^  <;nrct  centrom 
flium  gytant onm^ta  cbrp.ora .plan«tari;i| ;  atqQl 
omne  corpqs  gyrans  ctrca  aliMd  ab  iMo  a(tra« 
lli  »  five  JfUrminmrt  dAa  ajt  Sficejfum  (  ftcQi; 

«nijan  abibk  f$t  Tltmmm  curva;  ^  iii  e.  uni^ 


» • 


^ft  SiS^klJ.  f^mPt 


fi)rniitcr.MI  ^^m  )  ;  J^ii^m^fmm^n 
pUnerarji^  td  acccf&m  t  det^rcntoiiicar  j  |i 
^uo  ?  oifi  A  Sole »  ciixa  qoem  gyraot^  ^t^gf^ 
Omfirm.  U^  Omne  corpus  gfyrans  circa  ilio4 
orgetur  Vi  Compofira  ex  ri  proffSili^  Sc  auK^ 
tripcta  (vicie^*  iS^.  Schol  /•  )$  Vrs  centn|>ete 
cmcit  9  ijt  corpus^quod  ibla  vi  projedtli  im? 
puirui;ni'  ||ip¥ef ecur  axiifi^r^i,t^r  in  diredt^m » 
coqu^  iplo  e  c;emr#  Gm  Meedcret»  ed 'tlW 
•ccedat ;  ergo  corpii|(.  gy^HO^  determijnetur 
ed  acceflitm  »  &•  e»  «tt^fhtaur  %  i^txi^  attrl» 
^ionis  oomine  pt^ciC^  £i^ttm  enuncioi 
C^nfiam.  II.  Planet«  circaSolen»  verront  areaa 
temporibos  proportionales ;  quovts  tempt^-^ 
iculo  corium  verfas  Solcm  in3e(dcmt ;  mliori 
Cf^Ieritate  feruntor ,  ouai  Soti  (iint  vi^injores, 
Quam  >  cum  ab  eo  remotiorcs  (  ut  c*  requ^ 
dicam)  }  crgo  attrahm^tur^ 

• 

IL  ^hm  plsnetM  primmi  attrahunt  ficun^ 
Jdrhi^  q^os  iftorum  £iatfi(<i.  dicimus  ;  nani 
&  ip(i  gyrant  circa  primartps  ^  gyrati*una 
circa  terram  »  gyrant  4.  Citellites  ci^ca  Jo* 
Tcm  9  $.  drctk  Saturnuuu  Immo  :  pianefs, 
pcimArii  itiam  Sotm  mra^nip  tnrn  ft  f$  MUM4 
5^oIem  a.  plinetis  trahi  demonftrat  IIL  Ler 
motus »  (ive  principinm  aSitmis  ^  8c  raoHipmim. 
Planetas  fk  ft  mutoo  tr^ hero  evincont  notiA 
fimae  ilU  perturbationes ;  ccrte  Jupiur  >  dum 
Saturw  fitt  quam  ficri  poteft»  prpximusi^. 
ij^otabiltter  eiosdcm  motum  pcrturbat»    Simi« 

Cltf» 


ttirbatur »  ae  quo  hodie  iam  Inter  omnel 
Aftronornos  conirenir*  Idem  de  Dlaneci^ ' 
omnibus  affirmari  ,  probariqiie  poteu  argu^ 
menro  sb  anahgid  petirpi  Scd  neque  anato* 
giam  ifihuc  accerfere  opus  eft^  Res.certiffi* 
ina  fit  eit'eo  ,  quod  in  omnibus  planetis  ob« 
ferrentur  afferrationcs  quarpiam  a  ;K£'ibus  Kef» 
l^/^rij  unde  fir ,  ut  tapula:  Aftrono^ica^ ,  po« 
u^aquam  tempore  aiiquo  (atis' acclirate  cunl 
obfervariohibus  confenferunt »  uibuiife  diu 
lentire  inclpianr  ,  quae  aberratidnes  fi  nofi 
proveniunt  ab  a<9ione  mutu;)  (  J^c^t  iila  per« 
fnocfica '  fit  relate  ad  Sblem  )  >  unde  proye«  ^ 
liiant »  ncfcio. 

IITj  Denique  &  ^jiilanetd  Jicundarii  f^HcfA 
id  MraSliva.  '  Sic  t^una  maribus  nofiris  immi-* 
rente  aquae  attrai^x  verfus  illam  affurgunr  { 
fi^ne  L6na  perigxa  fir  ^  bene  atrius  e^van^ 
tur,  adauda  nimirum  ob  imm^nutamdifianii^ 
tiaai  Lpunari  attr^ dione  j  hinc  fiuxiis ,  &  re- 
fluxai  maris  pptentior,  Qiiod  dc  Luna ,  idem 
de  (ateJiitibus  Javij^  ac  Satirrjni  proprer  ana« 
logiam  eft  fiatuendum  ,  quamvis  eorundeni 
atrra<9tonis  efiFe<^u$  ob  nimiam  remotionem 
ii  terra  experiri  neqiyeahuiSf 


Prob.9ars.IL   Fii  iUieaiiraSivM  iwftofmm 
tc^sUum  agit  in  ratiom  reciproca  duplicata  difijntia»  i 

rwwt*     Planer«rctrc4iS(lteb  ferunriir  in  orbi- 
btis  ellipticis  ;  arqUf  dlipres  defcribi'  neque*^ 

ixnt^  fiiii  i^  cehcraitr^  pniitidet|QeatrraaiQ^ 

cor« 


« • 


»7^  S$6i9lL  Ofut  t% 

corpom  \n  mntro  niotas  pofiti  agat  in  tAtid» 
|ie  inverni  quadraci  .diftantianiQt  i  crg% 
Klinor  icapite  most,  (equente  den|on(trabitan 
II.  Celeritates  corporum  coeleftium  circa  So^ 
Icm  gyi^antium  nmt^in  ratione  inVQrfa  radi* 
^um  aiarui}!  diKlantiarum  a  Sole^  ut  K^Pih 
rus  detfkitA^  Eorundem ' tempora  pefioaicc 
funt  ut^  r^aiCes  quadrat^  cubicarum  diftati* 
Ijarotn  a  Sote;  atqui  nihil  iftdrum  ba^etl  po« 
leil'  Cii\b  memorata  attradionis  lego  (vide  c^ 
f^«)V  er^o*   III.  Spatiumi  per  quod  LuM 

intra  t  deprimitur  verfus  tellurem  i  eft  ad 
fpatium  I  quod  gravja  terrcftria  libero  lap(ii 
intra  idem  tempus  conficium  i  nt  ^ugJir4t$M 
^nim  fimf  t  JMM0#iri  urri^m  (  qu«  efi:  di Aantia 
iorporum  torreftrium  a  ejrotro  telluris }  si 
quadratum  [ '  ^O  fifni  ^  dimitttotum .  tirtiftriunt 
^qtiae  eft  diftantia  Liinse  ab  eodeni  centro 
terras);  ergOi 

CdraH.  t  lisdlem  ratiOAibtii  eonffcitiir  t  drHtm^ 
^t  (unt  e  genere  |>ftneearuih  v  vi  aitraBha  pP^iidttas 
§09  j  taqwi  agnoi  in  tasi^Hi  rniproca  duflixsats  difia» 
mamm^  ' 

CotiU.  It  liatitt  etgo  In.  fv(lemite  plflnetatiO 
mmua  afirarum  gravhat  ^  tam  ^ali  ,  quam  Ptahedsi 
Cometisque  omnibos  dommuntii,  quam  alii  jirtfviMiMi 

fmivirja^;  aat  giUiraiim  ii^pelkiilit     .    . 

•  •• 

SchoKX  Pofilio  tMfee  iire  4emonftrltta  hfipini^ 
CtMch  ad  explicfindi  dmnift.Coeli  phsiiomena  ^  & 
l^aomeo^^nm  airaimUan^iaf .  In^c  fepetuntur  om« 


4 


' » . 


* 

tm  Dlotttt  ealcftrs ;  iiid«  rtcio  de&frtftvrt  ^fkiMtil 
fccanhir  iti  orjbibut  elUpticis »  car  in  fwrir  «Kceanrid^ 
icbr  lenciiEnie  fiat  progreliio  i^pticlionini,  ^  iindeL«|ue 
IrregaUHcat^s  -,  )^rkeeflio  ^auiho^ioj^udi  |  flttXQI  ft 
^u^ut  imtxi  &t. )   dt  tdtiibut  »libi. 

$ft\  nam  iecMdniB  £«/i^fc^»  theoriain  greiistmsncuoi 

J*n  diiUnciis  mnjeribtts,  Cv  g.  pbqetaruni)  &  Cpniefiriini 
eqnitur  rationCni  rcciprocam  doplicatam  diAaiitiaroniL 
jh  qua  in  murimis  iiJhMu  pliirunum  recedtt';   quid  ^ 

J^toi^  etlaih  in  tnaxim&  fxarum  difiaHtiss  ab  eaT  r^ce* 
ere  poflit  >  t\xt  notV  iiifrctibi  itiam  tu  i^efUtJtaium  m^ 
Hri  pofli€  attra&it)  f  twt  dici  neqUeat  ftellas  fixat  pofti 
tec«fle  in  Hmitibua  coh^iionum  |  ac  jpreinde  coliec*^ 
timec  nmiuit  validiffime  tueri? 

ttlDtidi  (yftemate  bmnt  carpus^  cti^n  parTiah^.Ha^ 
Vrabtt  earpur  quodlihft  viribus  fnajpe  fuie  py6fmti9m 
mddmi  ;  (ive  t  fi  mbltii  «iiirpoib  iittrdnentit 
Aieric  tntjor,  vel  mtnort  cnarattttraAio  eji;»» 
dero  in  eadero  ratione^erit  majory  vel  roinor 
(  ettterii  pairibus  )  •  Prob.  Pars  I.  Omna  c$r/mt  | 
mUm  fartiali\  attrabit  ^uodw^  dHud.  Primuni 
lara/f J  crahuht  fua  partiaHa  %  quod  nifi  fiat  ^ 
globofa  eorum  forroa  incer  tnteftifto$\  eosque 
veberoehrifliroos  partiuro  rootus  cenftare  nofi 

S^tertt.     Geree  nUi  orones  particulitr  Ttlff^ 
ret  in  cetltruro  terr^  niterentur^  inque  tfkfti 
ftciderent  ^  terraqUeujrilksnofter  roagfta  {ur 
parte  jam  in  auras  dilapfus  fuiflet,    Pro  eSN' 
teris  cofpoHbus   totalibus   thiritat.  atia Wla  | 

Atik  roU  da«e  mMi  t^ifHi«rt  cosiiniir  t  qjj^ 

i^      .  %xpe. 

■  --^ . 


17»         smvi  ofMi^ 

•tperift  Mii  Itcer.    Vmmium  (eqOMfif ,  d«f 
#(}  reriuteiiFh  ^nTeffigandam  tria  erarit  efficltl 
ffima : jSnc.  praefidij  :  Expcrwuui ,.  if jm/oj^m ^ 
M$iBifi.     p^ficieptibus  aliis  Qbcipct  ^xi^ 
hgi4  9  ^ua )  ceu  Ariadna  filo  dudi  ^  nosinet 
«Tifti^i^  perkmlo  expodimui ,  yeritatemqtio 
fehcitw  afleqiitmor.    ^t  emmdiJkm  (recfi 
fo  Cbfvyft  Terba  in  pfaelat.  ad  2dam  W#«/o^ 
^i^i)  fi  dttroBio  urra  sd  &mfds  eorpirum  tftU^ 
ftf  j  &  ad  omnes  dijianiiat  propagetur  i»  Bn-opsl 
ytJnf  foeriter  fropagaH.4^0mus  in  i4meriea,% 
H  baa  rifftla  fundatSr  ommt  iMafifiia  » 
fH4  ^tka  fUiil  adfirmara  pefmnut  di  m 
Confiitutio  rerum  finffdarum  innaufififpw  dfie^ 
tionet  f  2f  experimenta  ;    inde  vefo  non  nifi  per 
fiimngaam  do  rehUi  ukh&farum  kdtitra  judi^ 


•'  \ 


tl.  J^ttioieHaeaUa  trahmt atiam  u^ 

Xit  altmut.    Stc  Looai  &  Sol  ucioiit  teri 
s  aqoas  marioas  afllirgerer 


Ili;  Partialia  mj^t^que  mporii  fe  fi 
mtrt^t^h:  Probati-onem  dedi  §§•  13.  &  144 
yfsri.tafiefn  bahc  eandem  luculenter  evincunt 
jfhkf^mena  cobaremis  »  eUfikHaeif  p  femmntam 
twfimt  yfolutionum  Cketniearum  ^  tuhotmm  capilU^ 
riiiM  &c.  j  a  quttMis  per  analogiam.argocr9 
Ilcebie  mmnam   partialiom  onuiium  ^avitif» 

$i9U 


\        rj 


CoroU.  L  CorDorihQs  nntbyit  tribm  pptcft,jai 
fl»  «  pantlis  iDstenain  conuitaentiBiis   danrsn 


^Qodlibet»  punllif  eletmmarihu  vis  Mr€&i%m  p^U^. 
itlitdf.  litm  ottiD^  in  lAolecuUs  >  6  qoibus  CQfpoMT 
troalelhintv  Cogita  AioleeQlfli  qn^viii  miOutiffiHias  ^ 
fingolartrahaitt^^  trihotniif.  =ASio  gruvkam  (  ina. 
tguit  fliictibt  Afo^-lMir^i»)  Mi  ti^p4rM  fx  Hi  prd^ir^ 
iftum  4n  ^ntgnlm  Mormn  form  toc^it  ;  «rfte  i^tiud  tfl^^ 
fuam  amfmm  immk  aSiofium  utk&io  >  t^prmnihgra^ 
vitano  frfQrum  HtfisfiiUnd^  J&  .n  gravitmktjfi  mntum 
Ifartiutm.  Gravitns  torf^ru  ttijusfum  i»  nvrmn  e# 
fortium  ejHs  grdviiattone  uajciinrs  t«8r,  ftia  morts  telk 
^tt&em  preMt  y  pendet  ex  ntjffi  yjiU  partiiim  i^rfis  telltf^ 
Hm  s  iemfffi)0erii  B&realis  grivitatio  in  A^rak  toUigjU 
^r  e  torpjomm  -y  ^niku  i^Jtitt  ^  pmnittm  aSfomhtf  ad» 
Vtrfits  itud\  y(  fi  mrram  in  portioHes  ths^t  itHefUal^ 
^am.cogitemm^  gmvkas  >  mafatir  in  minarem  orietu^ 
itjtngulamfn  ititts  partium  virHus  in  partes  fingtttm 
htjm  coujttndim  /tgetitihj^,  t^ari  ratiofie  fitotim  teUn^ 
rjiy  dempta  unha  pariicfiJa,  a&ioriem  in  panc  ipfam  par^ 
iicuUth  fpe^emus,  ea  tonJlhnliUr  >  rtJiquahim  omniuvt 
frsmtatt<mi  h%  fepfaratam  iUam  moiecuhnu  <)uari 
iptmvis  pairsbujut  globi  in  omnes,  ^  fin^itOs  almpar-. 
ns  :gravk^  i  &  oodem  argumento  f^het  pari  t^ 
mm  Sotaris  iujm  Syftematis  gravrtare  dicenda  efi  ffk 
lomuas  reHsptas^  t  tp^  imteufk  b^  rerum  cotnpagei 
ttip^git^ 

^iCdratt,  it  j^iiur  itkqx^  MuHui  Ofhidm  mitHd 
fftnBdywu  attraaio  ,  quam  SteTiPtoi^  v<>cabuio  baainl 
jnra^att^  gtnetale^  aJ^pelJimii^.  dihguk  corporai 
ttoi-pbriii^tat  clemehta  tHhuht,  ft  t«ihaft«R  fina 
gQla  gravjtalK  itk  fingula^ 

iProb»  IP«rs  )t  Omt  tiAf»  MrM  mpm 

mm^   Nun  lifigiite  cdrpon  ttmt&ui&mi 


nm  /• ) ;  ^fg^  &  fiognhe  flMlecolar»  &  Ongola 
pun^  materiaifi  conlHruencia  ;  protnde  quo 
nfiijor  fuerit  roole^ularum  ,  auc  pundor^m 
fiumerui»  hoc  major.  orit  accredlo»  Sic.wro 
corpus  (]uodIibet  aiirafaic  Tiribus  m^Ok  fiiac 
proportioaalibos  (  m$sfi  entm  didfor  niMariia 

Smamm  mpus  Si^i^d  i^nfiitmnihm  §.  57« 
hoU  1« )  ergo.    Cmfirm.  Annorarunt  AcsJg^ 

*  fMri  Parifienjis  :  pendulum  lentius  olcillaro  m 
itimmUate  moncium  Pirmviinjmm,  quam  in  eo- 
rundem  pede ;  noo  tamoii  retardari  wa£f#  /»re  * 
^idrsiQ  4Uf3s  JifiMU0^€$mM  isrr^ qoantam-i 
▼is  cercum  habetnMis  (exenphiLon«f.  l6i» 
Affm.  VI  )  grai^icatem  yerfbs  centnioi  ^irxm 
ad  hanc  legem  imminui  debere.  Pfaxhonfe^ 
lii  rattonem  aliam  non  reperio  \  nifi  quod 
pendqlom  9  eleyacum  ad  alcicudinem  nwi^ 
cujuspiam  cxcelfi^  retardaretur  eqoidem  pro* 
porcionace  ad  quadratum  w&st  dHlamis »  ^ 
mUA  c£0t  MrgHi0  mmiis  infirg  fatdnhm  jki;  3 
proinde  cum  in  dida  racione  non  refarde« 
tor ,  cen(endum  eft  montetp  fiippofituni  tra« 
jbere  renljbiliter.      Nempe  :  fi  montem  de«' 

.  jnas  9  atcrad:io  reliouc  cerrat  imminuicur  qui* 
dem  pro  lege  quadraci  auA«  diftanciir,  fimul 
tamen  aagecur  parumptr  ob  accradionem  ami- 
cam  fuppofici  moncis  cohcigui ;  hinc  irefo 
quia  non  cancum  e(t  aUgmtntum  attraAlonji 
propter  fubjedum  montem,  quanta.eft  dimi« 
nucio  ob  au^am  diftaaetam ,  retardatur  motus 
pendulij  ffd  mintiui ,  quaoi  pro  rattooe*4xa^ 
^uadraci  4ifi»oiBijb'     CosMludi.^     i    .vte 


w. 


'  pro9.  IIL  ReCic  (latQant  hodierni  ^hiioibjplii  t « r* 
trUBimem  C9rpar1i  iujiuUbtt  oriri^  acrefuUare  ex  d^ 
nihu  attraSioniim  ffecialibm  omnum  particularunf 
it$rpm  conJHtuemiUm ;  ftc  proinck  fi  naineriA  pmieiir 
krdiA  ftftrahentittfii  fic  ttiiyw^  vel  mtnor ,  iridem  attr*-' 
Aionem^  eflb  tnijorem ,  vel,  minorem  (kxrtit^  propor*^ 
tione  ad  noineram  partieohiram*  Huc  fere  reddie 
OitMiie.,theoria  ^rtfvitatis  terreftris ;'  ideo  enim  )ux(a 
f^iww^nm  corpdra  terredrta  gravia  funt ;  qui^  a  terra 
fVrillg^^i*  ftttrahuntur  ad  centrum  ;  ideo  ah  integrdtr^* 
hmtut  id  centrum ,  quia  fiigtila  urreftres  partietihe  , 
4;inU«  excepta,  rrahunt  virihoS)  quc  funt  direBe  ot  na« 
nverai  particiolaram  attrahcntiam ,  &  invitfi  nr  qaa« 
dratom  diftanttar  (  ftltem  majoria  )  •  £x  acerafiloni* 
boa  iUis  fpecialihus  oritur ,  ac  re&ltac  •ctreQio  toialii 
iprporom  terreftriom  verfiia  ceniram  ficrnB* 

ScM,  L  Ac  qtttrrere  libot  ?  fuf  cauffa  attraSict* 
nUiUf'J}ieHf/iu^n^  qms  fingnht'^  &*  fmnut^ima  corporU 
Cr^.  t€i^^'pa>'tes  exercent  ?  l^.  id  nallibi  explicatum 
dedit^Nrn^rdffitf/  Dici  ramen,  nec  incongftie  dici  po<*' 
taft  :  haVii^i)  attraAionum  caoflam  occafyfMlem  efftfi' 
hm  coexiftentiam  corporum  ;  caoflam  ^icientem  ipfum 
pEtfm.  U/;mf^  •  A  qu«ra(tur  ex  me  ,  quare  alia  ma* 
terttt  ^afficuia  crahit  aUam  ?  dicam  :  rei  iAius ,  flvo 
itiorus'iit  att^ada  materis  parcicula  caonfam  efficiemem, 
#(fe  Dflfilk^  ,'«d*^  qu6m  in  omnibos  mundi  hujus  moti* 
bos  Uicfmatlm  confagiendum  eft  ;  cfaufl*am  occafionalem 
tSc  parrieularum  coe!sifteAriam,  quia  voluic  DEus,  uc 
parridoiat  fibi  mocuo  prflt&ntes  mutoo  (e  (e  crahailt  in 
racionc  direda  maflarum ,  &  reciproca  daplicata  diflaa« 
tiarom* 

Sic  rcfpondendo  nihil  quidquam  abflird!  admfc* 

fih(r,N|uofd^#iminari^  l\Attit  Cartefiahi^  zxxi  Peripatetici  \ 

tam  enim  coeit^lentia\  qaam  contaSut  ^  firtimpaQm 

DeP  ^fEf  potcift  caujfa  4ccaficMit  motpt  -,  acqat  conta* 

'^  '/      ■  S  1  /  'fiai 


.\ 


i 


37^  iScBhn.  OfiaVI. 

'Ait  D#0  efrMi&  tMxafioiMlifi  momt  in  .eolUfibpibtii ; 
'crgd  &  «oefiftMitt^ffirpottft*  t^  Cv,  aiiMbo,  cor]m 
^iiie&?»il  poft  fiH.^pcrcnffioiiciii  .motiiiii  coneipit  ?  114- 
-flniliitD  iik  inftami  y^reoflionii  coqMNra  le.Xe  niiitiMfc 
tengttfit;  ^no  >fomiflw'pofii»yoU  QSnt^i^qcfcij^iintu 
^l^Iceiis  '^WHmvi ,  Jmiiio  ip&  nuHwnefi^  \*  it4^..Qr» 
tifm  y  St^Miblfir0Klf0  qme  re(ponfio  fi  nilul  ftUnrfUta* 
tis  cominety4M^'CoiittBetic  ooftre  iiie  :  f^xifiea^ 
thm  oorp^Yoin  efl8'D§o:  cenflMH  ocetfiomleiDr  pKO^ 
cendi  tn  utroqoe  corpore  tendenliara,  «nt  inqfqi^^jlf- 
fbs  fe  inviceoi.  Accedit ,  qnod  bac  caofl^s  oceafionalis 
conftiMB^-Miiil  oouiino  «dftroitvr.»  ^^4  iiofi  phci* 
nomtenii;  atMmde  6k  etidiimy. .  .Perifa$ftiG^jo3h\l,:jai^ 
too ;  bona  elilm  fide  paofiieof  (  ficilioa  mibi  :ftf rfiia* 
ierim  moi0e'0mnet  immediatcrii.Peo  eflici»  qai^  ^ 
occoha  tfHqoa ,  &  inpomtnat»  .qnalitate  Peripatcticfi^ 
qose  niinqoam  extitit,,nunqium  esifter,  ncqoe exifiere 
Dnqnam  poteft.  Si  pcoiicero  debeat  iiew$ott^-f  Sn  B§f^ 
hQvidlfii,  maiim«  Cm^kma .  Sm,  quam  Firifamim^ 

Si^iitN  4|UMatpr  i .  atr  V0lui$  DEm,,4^'^cfiirp(tmn^' 
toes^fiMMM  iMMywmmmm  mfftrum  ^ttra^iq^em  % 
€ur  totam  tttttnJi  frafinsts  bannfifum  bac  Ifgt^.al^U 
vit  i  .  Jff,p  mibi  uunptam  placuit  (  reeito  BotiLovicbium\ 
i/rr^7^iie  i^/MArr  fliMjfiem  cauf^ 

forum  fikaHum\tifm  ^  qum  tatmumutado,  #rf  madififtmf^ 
quaudam  ,  coutemphitiouemquo'  ujki  effo  arbisytKr  ^  j^i 
legetuatittgtuhinJi  fuuatueriui. .  N^  UH  petJtSii^i 
umfiis  itntwHfiire  nobit  piffims^^  qui  inmmu  r/trpm^s^ 
turdt  'ik^^Uim^tffi4vm,i  fid  eumuat  tansimmfla 
froprietates  quasdam  Ojptofiiituif  i  &  fii4SfOu^s,(^Mfos 
natune  ^mbor  potuit  fibi  propofiere ,  ac  propofuhf  duta 
mundUrh  iotidire^vidifi^m  til^iimtiiuOfUfi^ 

ScboLit  0ludia  uommtks  (  ibipfit  eouefim  Iqea 
Cit. )  baac-iufrokifi.caucltffioiiim t^  ^  occutm  .f|§/^ 

suiibw  uiJciQ  pid  miffs0th    GnaiHmnfcUim^cwss^^ 


IJtie  «1  Attrtaioncfii ,  ^mihum  efi  ftldjtrmud  arjg^ 
fM'fikHt\  occttltafvero  cmtghf  froeul  ijfe  abkgMias  0 
nihfofbh.  Hls  imtem,f(Uik  refponietur  s  oceultiu  ej^ 
eauffiu  fiou  lUat  quidem ,  ftarum  exi/tefaia  fer  obfirvum 
^ofies  elarigimi  deffienfirumr  ,  fiihu  fiiunp  ^  quanm 
accttltln  efl,  8"  fiSa  exifieutia^  nomtum  vero  comffrobatu. 
Grdvitas  ergo  non  erit  oceulta  caujfa  matuum  cilefiium, 
fiqnidetn  ex  jPb^nome^iistffleitfum  efl^  banc  virtuiem  fic- 
vera  extflere ;  qoare  dttradionis  oomine  quaiitate|Ql 
Peripateticafii  non  tndoeimi%    Mlluip  iflfudpeifimiiyi 

•vertiint  boni  Superi  1 

* 

Neque  eodem  nomin^  bmrns  intelligimus ,  tM 
uueoii  nugae  Okm  a  Gaffindo  excogitats ,  tit  gravitaten» 
cofporum  terteftrium  expliearet,    '  Henfiiritus  quos- 

-f^tn ,  AXkt0ttvia  eommlnitcimnr  \  fuot  Kepfleri  (bm* 
nfa.  Kam  quia  rationis  uQa  pollens  in  aoimum  in* 
d^tirift^  fiferi,   ot  tenntffiine  mpleeulCt  &  admodum 

'^les  liaml^^prsgMKtef  molea  in  terram  .co^mt,  (e- 
emh^e  abrtpitfnl?  onde  iiUi  nnta  vit,  &  emcacitas? 
qoid.^eft,  quod  iifiptSa  fiio  corpora  non  liirfam  im* 
peRant?  ciir  de^qoe  bami  ip(i,  &  onci  in  terram  re* 

'  rerti  eoguntuf  ?  AHa  de  ktnuf  ^  &  oncia  tkle  S*  i^« 
S^ot  III.  Oppofir.  llb 


Sed  neque  fttrifaCKom^  eum  vimeo  ^dum  mm^ 
fveffc*  confundtmon  Attwaio  eft  proprietas  corpo- 
*  nim  univerfiilti:  mi^etifmot  non  item;  tttSrtdio  tolU 
-  tieqtrti,  vel  mutirii  Itngoefeit-,  ficpe  immo  tollitoo 
irif  Mt^etict  J  tttra£tio  teqoitor  rationem  reciproctin 
di^ltcatam  diftantiarum^  ftqoe  exporrigit  td  difttlK 
t}u  pltnettrom  t  niliil  mtgnetiA 


^  Vcrom  qoid  ttttdem  eftirttr^o?  Eft  determtnt; 
tfo  td  tccefliim  tlias  expofitt,  quZ  quodfot  fcio; 
fuii  fit ,  tut  iri  qoo  fitt  fit ,  nclcio ;  «cque  iftod  fti^ 
Itt  om  lotcreftt  fireciumfitihn»fifOii€&iioi|  eedeia 


■\  : 


a.f$  :^iSkIL  Ctgiafl.. 

^tione  Corporam  gnrinm  motut  {empar  «9(pIarHb|.. 
idlciofbhim:  qaod ,  Gcat  attrabtre ikitae ,  io tiaoii 
.  iiliadtendit,  ^zattrabi,  qnod  in  >liud  icndit^  ntrqo^ 
'<]De  c&  primigmia  qaxdam  materrt  propriaof^  ac  pto- 
inde  nihil  ed  in  materi) ,  .es  quo  tan^uun  a  fftioti 
derivari  f-aiat.  ■  ■  .' 

Stial,  IIL  Politio  he^  .il^  confbndcndt  mh  ' 
eft  coin  jtritni.      Prior  «tinet  cqmprimii  td  corpbtif  ~ 
tttali*,  &  ad  exp^ivin&zmetuapi  eteUJUum^X^dttmwi-'' 
ii«  I  poHcrior  fld  partialta ,  &  aJ  cauffikt^  ^''^ViV'',  '^!''- 
ftrnrn  terrtfiritm.     Sont,  qui  tlieortam  rte»i<«t/'6tf'rtP  "■ 
iHotQi  cxlcAes ,  &  artvitatein  corpotoni  ^letlium  am-^ 
pledontur  :   rcjiciunt  circi   g^vitatcm   tc'«ertnliSi|^  ;' 

Jirimxqne  politioni  veritateni  Ibtm  tdjodictritViioa"  ~* 
ccundx.       Priore  o^ta^xtaT  at^amoutm ,t^t  f^^Tf' 
ti4»»  reerproca  diiphAtta  difiaittiarum  :  pofteriwfi  "ii  i*. 
,  tiam  4ireda  titajjarum  titrabttttium.    In  prima  nibil  ad 
quantitaicm  at^aSionii  conferrt  vidctnr  niai(S«.at(i'»;..    ^.^ 
lientii.'  cohfert  in  lecuiida.     pono  enim  ( ^nod  linse- 
t<aat  GaUorum  aliqni )  qugniitatcm  attrKtionit  iEfliii{*>  ^ 
tijohm  ex  magnimdhtt  vii  fejtdeiait  in  timho,vii  y«'^ 
ro  ex  magniiudiu^  vtottu ,  ,^am ^  imfrimMw^o _^i^ 
ma^ria  iuvi/thiiiii   «{  ceiitruiu  torporis  vijStnii   >mM  ^.,<a 
fnptUtnt ;  ttit  profefto  u^trumqiic  iftSd  a mafia denfio-,,  ^^ , 
re  vel  rariore  corporis  attrabcDtit  omnino  indcpehdetii ; 
quo  cafi)  falia  crit  ^ipfM 

dit:  vim  carptrum anraSi  „^. 

tta  mi^ro  ptrttcuUmm  at  ,  '„ ; 

^ltam  efle  pofitionem  ft^  ^."'^ 

iim  graVitatii  a  Newtotia 

phznomeni  caunam  ;  at  c!  ,.,. 

va  manebit  omnis  theoria  Ntwtont.  .  , , 

CmU.lK  Prima  potftioneevianmdiril^riff/ii'' 
MM  carfrilmi  emnihus  totrmtuutm  ag/irt  in  ratioier*. 
•jprMf  4iflieat4i  d^ifi^imvmi  foci  fi  «.tnu^ooem  , . 


r.rt' 


«««»  effir  fropor»<mAULm  mafpt   attrMbmti  \  i|iure.  ^.  / 
«ttradiones  corporam  nec  cqiialiter  ^  a  corpore  attrt* 
hendo.,diftamu]in,  nec  cadem  aiaf&  prsdii^niiil \inv«- 
cem^  con&i^^ntor ;  tam  maflarooi,  qoam  diftanijacsftili    - 
rationeoii  M>eri  pport«bit.    Brevitcr  (  fi  t^afTa  ^tfraheHk    . 

h.  e.  ii^fi,attrfl3iv^  trum  in  r^ti^uerdir^A  fnaffarm$ 
Bttribtntiumy^miprQ^.^tifhcauj^^  -^ 

Dp      U 
ratiaae rjtflir^ji^iitpUcaiia  djfifmtifrum 

lom  bhiiii^^rpQa  grave  eflety  ni(i  attrahere(iir  aH.eOi» 
in  qttod^jp^ayj^tat.      Hic  vero  ^licite  di&ernendum  e(^      ^ 
OtttraBtionqtp  infejr,  &  gravitatem  (  (ive  of  alii.vocanty 
ittraQjo|pe|i| JntcF  aSivamj  & p4jpvam).      Priof.refi-     . 
det  in  mafla^frtf^Kfiirf ,  in  qoam  tendit,alias  pofte^lpc 
itt  mafla  attraSM^  qoc  tendit  in  atiam.       St  attraSiai 
firtmi|^.,^mirom.ma(Gunim  4^  &  0  comparentfiry 
crit  vif  ^«dtrahendi  v\  4  tA  vim  f  ttrafaendi  in  S^  ot;     . 
maffii  4eAB  (paraNU  diftaotiia  > ;    feo  erit  V  i  v  =3, 
Ml  19  (d^^g^  «otem  per  y  ittraftioocm  corportc 

S  4  •  A 


*'    wu.*^» .    -V 


1 


I  .* 


fti«it^i3ftti?f  gJiVittiitrorporh  >td  gri^ifiUetil  cJdr^ 
fotu^B^  Scm  ^iaaAcorpons  AaiTnaaii»  corpo. 

4^  dkamr  F,^  iilc^uit'ii ;  fiei  »^^  V  d^  im  ^  M.  Si 
4ttt»tito  («d^  ttiiffiir  im  ^irnl^^  j^jfe  ^«ii^'^^ 
vit^kutn  ^  &4fiS^giM^0lias  |,  k  e^  mtfli  ^  kt  corpiw 
Jii,  mflfa  5  in  ^,  eric  grtvitas  miOl^  — ^     -  ^- 


tcfl».<niaflkift»  ficQJ^^  corpai  M  td  m;  pcoiade  l^ 
ftiAclde ,  &^^ne  i^.moleftUoi  tiiquclegedfiol^^flU^A 

?S^   .^^"^  vl  |fl?W.  llfti  ^fit»  •Sqibi  ^J^:* 


i.,^-,p4  vvnr 


tyrp  ^  fBi<f  jtirer  -  Jl^^^ 

iSi.  %t)fliii  arqiMRcitkr  nm  fndf^^  ki]'^^^ 
fQt  c»lk  tafljtiCin  ^oti^itibW|^i<>li]^^ 
«•tionfei^fi^nefo^dfiMaiit;,  hi»c  IT.- 1»  sf  *^'vu^| 

^tib  t ftripff  mxm  P^i  ^  W  ^  <  -^  )  miUttih  hM 

DI>    M 
^  imiefttQi;»,  five  notneratornm  vator,  tk&  mero  ^ 
licrminatorom  ^    jf.  QQii  per  oaftiites  illaf  %iifieitm^ 

i^  «Qamitiii^ioli^m  c«nAA«c«0i  ^  cQjoi  ioeo  flk 

n 


i- 


^  i^tfii'^l>9  iU>rQgacipoteft ,  cum  aon  SNi^tiii 

•  •  *  « •  <A»        w  • « 

Jhili.i  bi  W  iW  «»»  ftou0«.  wioiwi.  Wiiiinpi:  die 

•il[#rft^«irnw»  l«ffr    -  '  ■;.    n 

'<■}.  sLrAotu  ■.*'.■:■■'''  :-»■„  -■•►■•■•.:■ 

Qocret  lu.  Qaifirt ,  Ht,  fi  fiwsB  --t-;  -^  , 

l^j^fK^nm^-  pnmyytarM  ntioaem  direCbin,  divnQB^ 
^=*;  ^''^rirpbife^iife^i^^a  ri»Pa  F^ecenia^ 
U\in  r«tion«in  cqiMtntce  tten  ^oteit  ;»«r  nxtom  6^  §■ 

dum  perinde  {iie|^  five  aict«  e.  9.  atfr«mwes  effi  ta 

Iftq^  qa&i^ayww  «riqqtvtnttaimiuri  «t^  probe  aot«> 
fnwvHinii  i-;^.  .-■••  .    .J- ,.,;..  .■:■:■ 

Ncc  iiilnui  |d ,   qi^od  ftqnitur  J  s\ximt  Phjfici 


i 

•«,     fUtio  «ii,  qai«  —  I  -r-  5d  f ;  7,     Itenwl 
■1  .  ^  .    T   .  ■« 

$1       -X.     '        ^xom 


t|ll  SfShtL  Opal 


Mtm  fccaoclafn  pcr  nSiifii  cv  Aiiid* 
■iit<lrtiltif"1gfti[ifr  r*;  obtindifi^-^r-^^  '— r 

r 

re  Ijmmnm:^  fi*  — ^- 1  >—  =:  •--.  t  ^9  acUbripfi 

<-.  •  .  T       f    .    -T.  '•  -^^-  '  -^        *    '- 

iciUtfet  nmiBie,  qac  iliat  ucitc  abivis  inccUigcbttor. 

t^^t^4«  Pofita  aniTer (aU  te^,  qiiod  qoas^  ^^ 

tiorfS^i\¥tA^  miflarum  artrahcritiflnt,  &  rrf- 
cipf^  dapHcarf  diilantiarum^  of>tinerrde-     , 
bedtparticulafes  aiix  leges ,  ut  Yequohtur : 

tEXfms.  &  punSum  cxtra  fphMrMi^  tUijuM$  ^ 
B$9tm(nuam.fo/kum  m  fingubs  ^usdcm  fphar/cfun^ 
MU  trdbMir  in  rMiom  'rcdprocs  JupIicstsJiHd^fMM^ 
wum^^r4iiCuf  pcrindc  a  tau  fpbxrcfl  ^f  Ai^4^^f 
wstur  'ih^  raoianc  ruiproca  duplicata  fiUut,  ^^m^t 
^iccniro  ojusjcm  fpb^^;  &Y^%tpUEiiacfk£pbf^oc 
tm  heiMgWM  panes  cMiein  •iiiodoc  tci3iii|ie  , 
sc  fi  in  ceotro  fphxrae  coUeftx  eflent  9  rel 
tan^uam  fi  tota  yis  promanaret  ab^iinicopan?^ 
Ao  in  centro  fphccrx  cohftitutb.   [,.:.'\ ^ ;,   ;  -  ; 

^fii^.  Finge  totatn  fphcram  ifi  ceneroiilM^      ^ 
condenfari;  qoantum  |Mrtes  hemitpbvrii  an^.   v 
terioris  a  punftp  eitra  iphxram  pofito  f^co; 
denr,  tihitondem  partes  hemifpharrii  altefitls'     ^ 
Hd  iHudacfedent;  proinde  qoank^  ekrVt^''' 

ceflb  uhius  minttOB^la  erat  ittnftio  oh  au^an 

di- 


augtndi  ^  Droptcr  minutam   oiitantiam. 
Jgitoiv  .  ^^ 

ram  recidic,  diflmrH  lajptdit  attraSi  ^teperenda  notrT 
cft  a  laperfieie  ittme,  wd  cb  eiaidem  eemro;  nofi 
«maiflm&&p«feictlMidem  trahif;  6d  ugrmymf,  ' 
coiDS  attnfiio  coiUcfiim  coocipinif  in  ccntrofcfrc* 

^SchL  it  Sphcra,  cojaa  mcoiuii  ^  om^otom* 

idiftribotimie  ure  ^a  maflarom  hompgi^eit^juil  accc-i 
ditor  i  qviar^  qoat  cle  fi)h«rif  hoinogeneis  dico^^  9Q4W     . 
praxh^e  ip|»li6iH  pofl&m  tiellfiri;  Soli ,  't^khif.  ^,  J, 
ionc  taoiien^pbainb&eaorom  attqoa,  qlue  "tt  luittbU^'  ^^ 

nem  camt,  Ntwtomm  adeatj^ 

^IWicli^'ciem6;nttrat ,  qdoc 

fpbctii.^^^^^^finc  ififro6h]di 
rario«;ipJyq[)li'Mim  (pfccra  o^      ConetjA  ^flarb^tp. 
finitii^  ApaAcicboi  %luBricil  >  coaocncrtcic ,  &  homo* 
l^ncpw,-^       •  •  ••»•',   '•'  -V  *•        * ,-     'j        '•  '    ■  r-. .> 

j!^  Il^  Si'^  ^mi  hompgltic^  j^naon^ 
ktlc  6  motoo  graTitlrCi  ^iaWiabonr  in  ratione  reci- 
0roca«4^im«'cwr«wr^  'temfttn^nl^  ^cra  cook 
tipi  p9Jitijyp«€aMpt€Oi|dco(aoi^  j  :  - 


.  ter- 


idtpmBtm^n^BM  ihijtntiH  'OUkpavii^tS,  Pro6« 
'Q^cunque  )6m  ^f^dflatf^ipMiid^  ,^  leAipcr 
^ii^jop(k)fita&,  hinc  &  niinc  agcntcs  ilMmr- 
ttld^  mcfehrl  Nahi  primo ;  fit-  pjGiy^^iim^  coiw 
^icm^i^^ltl  ^entird  ,fi»!iakr^    cujusdam  Vjw 

(fig.3Qi)jJ».apcxtoc(t:  exo^nipaiftr|c<jua«' 
btcTMtriihcn^m;  pr|(^iii4ft^Y^^^ 

fi^iirt^  tfife.^  V  Sit  fam^tn  ooiicrtim  iii  iiND»  | 
^V'#*^'^^^*^  f}r%i^ppBfite>*int^Bc^i« 
ic  igehres  aN}aa1itintttr,^rae!>.^u^  fe  efitfencH 
4Ufohm\  quod  pdtiaQY61toet6(;ya)nftitis^  j 
,tt|Wa4  pn;Wi -P^rtco!!  ^^qedat  WaflWa  i^uim  ^ 
•dalcerdminQVant^Aniai  n9a|oreu  vjf^piio- 
^toromr  Mopiw<mi(^uam«f«nio^ta^^      Kanto 
major  cft  numciug  mMti#riH»y;<g«iiiiitr^ 

e*drtim  j  4ii|)Ci^iialo^9iristaviiicretiienti^  ba# 
ifi  idetief  eiD^pirte^  itn&  Afa^^inQB^f^ 
)^m  )[]iftantiati)^  rale  pcor(^i'hi(^l  Qcboc  cx 
altera  ott  i^«rcnilpiiiiAorimi  nliiiiiftrtito»  U 


/"  k 


•Dguii  id  verticem  bppoiiti  ^9u#|ef  j  t^  i^^tH  A 
ss  P  y  cutn  amKo  ioU^c  eideQi '  arciiiN  CE  £  )  qwM 
^:  DBzi  CBtDP.-  Jmne^AtmfmStaBc^ 
dpiantur  dtici  inniioieri  radii  ad-  ifegOieiita  lAtnima 
jiC^  &  DBi  orienoir  fncra  ftlidg  fimilia^  fa.  ^  py^ 
f«mide$ »  aut  con^U  cuipidibot  in  P:  fihi  motaa  obvfOi 
fi  4  ac^ue  «deo  ba(i.m  htbentes  tmv  in  ^Miento  yf  Q 

tNm  in  oppofito  Oj9^  corpoconi  anttfii^^u^  ^ 


' »-  / 


« • 


aQiji  fiKdij^nv;  ^fib  '  ,.^t§tfi  \*erp>afct5  flS^^  .^ 
illtnc  polst«;l^gpantina^u«  uu.  ^t)(^itHrfKcni  matcfiljfc 
«X  utjraqttf  mm^MtxiX\%\  ^CPaotcm.  &\0P  n^t^ 
diftwks  («ia^^ofc  arcw  njftiiW'C3*'ia[  A>'  *ifiJP 
=s  F  (i  >;  iergo  fi  'quantitas  maicctiL  te  jatt^  ;*CWJi«* 
tis  clicaturigr;  Qi^  part«i>iB  Agcttdsilifplm^^S^ 

^yf^D Dr^  &  JQ\B  ^CP^tzy44^^^A;i94f^Dt> 

quar  vim  s^traaiya^  a^eiueiu  isx  ))^r(c  0J$>  .fnnt  ctiiia 
attra£tion]N  in  raciphc  compDflra  ex  dlrcda  inafftf ntti 
attrahentiom  ,  OC  rcCi^roca  diijplicata  diitamm^um. 
Corjnis  igitur  ?it'-j*  ^ociituin  iial!a> ' fi*ft '  eravltelit 
icntire  ^Otcft,'^  i^quallftas  fcilicdr^attraaioni0OS|*^»*e 
4ia^etro  <)p|v4li$'<^  clidchcibtMi' r  ''"  ,r-  rr^ 

fiigid^M/mguHf  (eoC4  pua^knifi  li < ii|  fpti^d 
i«{Uki(^f>'  <c  «.io;aHa^  ialid«  #»  j%.  9x0^^" 

fertfht  sdMttmbs  cti|ttsQtie  bandi  'j  cenfro 

a^  at^i('afi^^i#fn  V  ^f«^ 

Con^ipljiiipi^l    yim    actradivam   Cngtilardnl 

f\Aiimwfi,t^<dtu  in  cemrts  Tufs  (f.  i  S^v)» 

*  Mm  dtftanti«rO:  pon^i  4  t^centro  fno  voce« 

fbufr  D  a  Jk  8e  jUterius  piindl  d:^  f.      C^m 

-       '  Jlf     ^  M  .  \ 

ur  afta/  ^t^  bmnii  attra Aio  ;=;  -^  ::=:  — ^  i  tAt 

DD      RR 

Attra^ia  folUmr^^ad  atttai^io&cm  alteritis/| 

'  SCut 


n6  S0UV.  CifmVti 


ficok:'(pAa(r:^  <f  diirTfa  per  quadrattnn  fadti  ^i 

44 f^^^W  /ii^rum  qiviia.in  per  quadratom 
k  i:a0u,^u  ^  .Sutic  autem  xion  minus  (^hmfm^ 
"  ^oaa»;>Uil3  qoMts  (blida  fegolaria  in  ra^ona 

triplicata  dtmenfionuni  homolo^arum  {^fwt 
.  Snr$9m.  ) :  proinde  fph^tra  S  :=:  /t^>  8;  i  :r  r^ 

qtni  talofe  riiailis  ibh^ricrs    fuhltiuiro  fiet 

ir;,«  ':is,  T**:^  5  ---^  ^  K :  r«    Significat  aa« 
tf^  r.^teraAionern.         '. 

Cfn^/t  I,  Si  pundnm  intra  fyjfixrm  (blidam^  'flc 
fomogppne^m  cotiftijcpitur ,  c»  c.  in  P  (fig'  :^^-^)  lex 
Cidem  o|^/iiiere4«btti  0»m  fi  inrcrvflllo  ^Pdercrtbe* 
.  tor.(|»ticra,prior|  cpo^cntricat  jMitidom  ttr  f  noUam' 
vim  grav^atis  femieCj  ^ea  ratiopf  &i(i€C|  ^bsr^aiice* 
riori^  cavz  (/.  prdc^-^  re(U(  ergp»  ot  U>\$  iiitcrior 
iphxra  ^t,  cQJoa  atrraQio  cft  io  lactooc  ttdii  S  f 

« »  .  - 

arell.  It  Qtio  propiiia  >pimftaiii  ad  AhoM  jb* 
Udc  cemr4tm  acfeficric,   boc  minot  jcdi^  dabct.:]i^jD»« 

dcm  Q)li^ca crtraQto ,  minnitiir  ciiim«adtiia»    .Cm^ 

iraj  qno  magtt  ab  eo  rcceflerit^,  Jboe  ^mi^.aritvia 

a^rra£liva.       Pnndam  in  fupjefhcif  ijdi^ie^  (biid*  po> 

£tiim  maxime  diftat  a  centro;    Dlic  crgo  attrcbietar 
maximc.  •     ^•.  «  •  i  .    ,-    : 


s 


"  '  '       r.i 


Coroff.  lI/«  Etiam  io .  CQoia,  pjrmoiidlibtit,  at- 
liptoidibos»  cittcria<lQf  omnibaa  ro}i4ls,^iiiH^ 
tra£lionea  (imt  in  rationei  direSa.  ^upniQf vis  iaceroaa 
liomolo|orQm  ad  fimilla'  {olida  'pertrn^miuoi ;  qW 
•nim  rpnicria,  eadem  pUnc  demofifiracio  oinmbQS  ($- 
lidia  fimilibai  acConfmodari  poteft.  .  CoUigei  i  etiaOi 
ponfta  in  fiipcriicrebas  cUiptQidida  pofita  .grav^re  ta 

fiinQac  dir^  diftamiifrmtf  ctcnfro; 


SkM.  I.  Thcoremitu  liu)«|adian£l«r  ompMi.iil 

fic  diram  ,  peiincicki^  efl<i  ac  mtime  (TefViUri/detebr, 

'(•cd»  ficilc  conftindetur  Tyrb  ■,  tiL  ei>  tttiiipVJAiJi,  \inoA 

gAirn: Mfia»ti0^rHm.   •  Siuir ^  itpito j; «rvd udea* attfMn 

■f  •  .1 

,     '  .     -  -       ^    \  ■*/,'■'  ■         .       «»'   >  1f' 

SehoL  It  ^  Qui  in  caufTi  gtmiiw^  'wXrm\ ,  fluC 
iidanr  ver&tl  (iint ,  leqQentes  leget  ictoitiaem  jprci  bcti-, 
lit  babendfli  efle  monent;  L  OnmU  ci^rporg.faBpaM 
mg9facin)4'f  ifa^m  in  certis  di(Untii$  exerttht.  ^  ProKt* 
r  ai  ixptrievpa,  ^  auahgia,  ,11//' jlttr^io  cor» 
^  mm  efi  nmtuas  occafionalis  enim  eiiiiA(tktti!^dibkiia 
di«i  foveft  cioCMft$iit«d ,  qmriempdr^mt^ua  tff.^  UL- 
FelMtat  ;- \iiir'i/V' '  qna  corpuiuunfH^abh  dfuU;-ch' 
teris  fariiufi  fH^  antajfa  iC0tpefif'dttrallfinHi,/itii 

{>rop0nioiiat*'eA'^  fint  thim  iedvpor^^^  &^S  i'1iinhAr 
ibii'  UKlii^ ^&^^itberur  corpu«  B  th  j4'(per  feg,  X); 
"icoi^n  iitf^adtatul^ati^  Jibra,  jrtfamJfla  trlKer  ctlrjiuf 
^"t£S(>  dbw  eUt69^ffiiti  <]aare  forpaS'  B  in  iKkiL^hypb^ 
tfaefi  1  rahetur  vi  duplici ;  ii  aliam  adhue  txhtemi.  adji^ 
c«rii  id  /f,  trib«tur.S  vi  triplici,   trahent  enlm  librc 
,fiigat»Vl^<t;<^^i*  ittr^divft,  &  velbcirtcRi  prdjportioni* 
'  tti  tft.  iliiflki«tt|ralieiiti.       IV»    Felecitas ,  attt  vis,  'ijtiA  * 
^Tfus  musk-frabf^  at  alio,'  non  peudet  a-ftiaffa  eoh 
farirmtfaSti^'  i  c.  corpua  atrradum  eaderii  (tmpeir 
v«lodtatt  ni6Vehitar,  fivc  fit  niaju$/  (ive  miAns;  vc- 
iocimiHa  pendet  Uni^c  a  mafla  corpori»  itt^ahcntis 
(  ueteris  paribtts  }•       Sint  enim  priora  corpora  H  ^ 
A^  lainbo  libram  unim  ippendentia ;  trahetur  iterum 
•iiqQa  tiy.  &  v^locitate  corpus  B  ab  j1;  coi pori  atf 
mAo  U  «ddffttir  )ibt^  una ,  qu«  cpm  coexilbt  co^« 
t^i  jI^  non  minore  vi,  Sa,  yelocitate  trahet^r  ab  /^l 
^iiaai  antea  corpus  unin»  librat  ;  ere;o  velocitas  ejul^ 
nec  aug^bltur»   hec  minnietur  ob  adjeQiohedi  ufiiui' 
librs;  &  fic  ddn<:c|is.      Qdare  corpbra  ooinia  (c^f* 
iririr  paribttr^  >cidem^V^!ocitsJto  trahtimQrv.  five  jW 

j       jora 


j^a  fiot)  fitt  ttinota.  Lcil  iflft  plimo«iiiiil  ifrMli 
fiMuneft  I  €«fl»  Jtifffer  cadem  vdocitm  tnMmr  n 
itfoie,  qnJ.^SJyrf/iiiiiflira'loogeiniflortt.  V.  f^c» 
Inim^  »Ht  vis^  qim  torfus  mmm  tlrAit  ofioi^  i^  ai 
riMMM»  ret^ocs  AfUegM  Jiflmaut ;  m  cnim  itla  ca» 
ilem  cft  com  vi ,  qoa  Loita  trahioir  vcrfiia  arllorcia  } 
atqoi  b«c  cft  in  racionc  reciproca  doplicata  diftantijl 
o^  «aiJrro-reilbria;  ergo  A  iftiu  VL  DifimiiUt  t^ff^ 
fmmfife  mtraitmium  neu  €  fiperficieitu  ^  fid  oi  ce» 
fWtuUm  mmris  mfmmiit  fimtk  Scd  de  omuibut  iftie 
jam  iatis  dixi  fiifHra »  tpm  eamcti  Tyronibos  repoctlriflil 
nofi  |ft  rcm  inntilcm  cgiftc ;  fic  int!||ligcnt  omi 
ibcoriam  gravicatis  cbrporite  five  utltfiimHy  five 
rtfhrimn  ab  hia  pottfltmo  tbcof emacia  n^eteadam 
Hie  prmifflia  fit, 


>» 


%.'l6%  GtsiriiMs  pra/tcifk  nm  potefl  d im»^ 
jf^il^one  maima  alieuJUs  fiuidd  per  univerfum  J^fk*' 
fit  ( quani  Cartejius  m^feriam  fubtiUm ,  yel  snii* 
umt  appdUt)|  five  illa  circa  globam  territ* 
qvMum  in  circulum  fluere,  i*  e*  aiit;effMMi  oa* 
l^  ponatur;  live  dieatur  in  Itiieis  redis  o4 
rerram  iugiter  manare)  &  corpora  fibi  iona* 
tantia  rtSHlinte pr$mere ;  (bu  deniqoe  motte  qtto* 
dam  v^atori^  a  DEO  impreffi>»  8c  virfits  Ur^ 
r^  cesitrufn  vtlocij^me  propagato  obvia  qutqu* 
corpora  in  terram  propelTere  fingatur. 

Adverfits  fonmfrimam  tuiSkant fequnMat  ta 
Yertices  ilii  commentum  funt»  quorum  eiti*   jj 
flbntiam  fufius  impugnabo  Pssru  lU  ad  ciufl&mi   ^ 
motus  aftfortim.    11.  Si  materios  illius  VortU 
l(0&  ekiftet^tia  dltro  tribuieur»  adhuc  taAeil 
OuiTa  graViutis  efte  tiequit;  quoeiiim  pafta 

«prpora  ia  ttrrapi  j^opelUt^     ^nmftrt^ 

Cir* 


< 
t  ■ 


C^uJtoHii  fioidnm  hoc  ob  MtWzm  fiiam  t4 

tnocum  apcicudinem »  6c  ob  imnianem  fevo^ 
jucionis  ru«  velocitatem  (qu^  jyes  majored 
yeiocitace  tnofsjjs  dairni  Jelluris  )  concipit  vim 
Gencrifugam  adeo  v^lidam»urcorppra  •mniA 
fibi  admi&ca ,  i}uorum  iniaQr  eft  vis  cencrifuf 
ga»  miriorquead  motum  habtlicasi  8c  «ajor 
fnercia^  infra  fe  detrudac.  Ontra  3  S\  canft 
fit  materiat  fubtilts  veiocicas  in  ipfa  Juj>$rfici$ 
Urraj  quomodo  non  corruanc  #diBcia<  non 
radicitus  evelluntuf  arbores  ?  Cedunc  ifta  ven«- 
^orum,  curbinum  9  ac  correntium  impetui : 
quomodo  cam  valiBe  fe  cuencur  ^dverfus  ve^* 
locitatem  lyes  majorem,    Argumentum  iftud 

Jjuam  maxime  urget  CsrufioHgsf  ^ui  maceriam 
ijbcilem  cattcris  omnibus  terrenis  corporibui 
denfiorem  clle  palam  confitentun  II.  Qjio* 
modo  fubrilis  h«c  mareria  dum  in  excelfa 
quaepiam  corpora^  e.  c«  in  monttt  canca  velo* 
f  itate  impingic,  non  (enfim  iilis  motum  fuum 
^ommuhfcatl  quo  pofito  vclocitatem  cerr« 
ab  occafu  in  ortum  gyrantis^lingulis  diebui 
«ugeri ,  brevtque  celer itatem  materiae  fubcilit 
ad^quari  necefleeft)  id  vero  fi  ftac^  cbrpo» 
rum  cerredriuni  vis  centrifuga  dequabit  illam 
inacerf^  fubtilis;  non  igicur  ab  ea  decruden* 
cur  corpor^  tn  cerram*  IIL  Quomodo  gft* 
via  omhia  non  ad  axem  cerra^  dtriguncufi 
fed  fenfibilicer  ad  centrum  (  fatentibus  Caru^ 
fianij )  com  camen  a  vortia  ejusm^di  grmjia  band 
$d  uUurii  dntrum  ^  fid  ad  axm  ipjum  dirip  «#» 
€$J}$fmt%      Cum  inim  vnu^  ilk  i^  iiriuhi  mS 


A 


squnorm  pirMcUs  ftutrti ,  c§rpors  grMvis  mJ 
runJem  circulorum  tentra  (^uaptr  totum  uliurrs  " 
sxcm  porriguntur  )  dctrudtrc  dibtrti ;  nr^iif  dim  ^  ^ 
-^u$m  €4  corpora ,  ^ua  fuh  ^^uatcn  firent  pofiu  ^ 
sd  terr^e  eentrum  niterentur.    Boikovicb.    Opp<M . 
litio  i(bi  funditus  evenit  dogma  CmefisMrtem^ 
qoam  ut  rite  inteirigas,  adjicio  figcrmn  3^«^ 
ubi  refta  Af  ^Vaxem »  circulus  A  C  «quatorero^ 
circali  DjF,  9/matertam  fubtilem  in  circu- 
lis  «quatori  parallelis  fluenrem  defignanr, 

Adverfiif  pMrtem  /7.  £?*  ULfgciunt  ift  4:  ex  Car^^^^ 
tefii  fententis  materia  rubtilis  permeat  omnia  ^ 
Corpora  ;  itemque  ex  hgtbus  ftuidarum  xqu^XU 
ter  premit  \t\  omnem  partem ;  proinde  quan- 
tum  fiiperior  fluidi  portio  corpus  iibi  inna«' 
tans  premit ,  tantum  inferior  (omnia  perv  1- 
dens)  reprimit;  quomodo  jam  corpus  bpe  m  1- 
teri«  (ubtiiis  fuperne  preraentis  in  terram  de- 
trudanir?  \l.  Si  materia  ifthxc  fit  gravita* 
tis  caufla ,  quo  corpora  terrefiria  majorem 
hi^ic  fiuido  onerent  luperficiem ,  hoc  gr^vio» 
ra  efie  oporteiMt  ( nam  quo  majorem  habe^ 
bunt  niperficiem,  hoc  major  erit  numerus  mo« 
lecularum  astherearum  contraip(a  impingen* 
tium )  ideoque  y\s ,  qua  ferentur  verfus  ccn- 
trum  rerrx,  erit  praportionata  fijpcrficie:);  - 
:ttqui  graviora  non  fimt ;  certc  cxpericnrra 
docemur  plagptam  cbartar  r\tc  in  vacuo  j  nec 
aSre  libero  celerius  in  rerfam  decidere^  quarn 
cxile  plumbi  frufiom  infpbaram  formatum  j  ' 
crgo*  III.  Ex  hypothcfi  flnidi  alicujus  ad- 
,modQOi  clafticly  fcd  is^i0if7iii/|  qoaritnm  gr^ 


•  \ 


W4  W^?&ftHi  per  <?jusd«hi  flutdl  fttjtefbris  e«r 
iurfus  v^i-fliJ  tet-fdoi  prbpejllentirf-i  ptt  aU' 
temos  fluidi  infrrioris  reeiiirfus  a  ivrri  fepc!*] 
lencur  (  deb^nt  6nim  orciilaciones  macerijt 
Kcheres  arque^fortcs  eitetnfri^  u  rupra  cor«^ 
K1S  rerreftre^  cUm  tn  elafticis  tittinibus  vis 
eftitutiohis  arqualis  iit  vi   coiTipreiiionts  )| 
titlfiqaaitt  tf go  corpora  in  terram  recidenc^ 


f. 


Scb^L  dici^s  1.  Ih  bypbthefi  o&ilt^tiohtiM  itthu 
yftaruih  ut  pririuim  corpus  iib  ^tbierc  dcorfuih  ckcur. 
icbte  Vcrfits  ictHni  iinpellicrtrj  cdhtirtUo  Vith  cbnci» 
cit,  ihoitK^iirbquc  fud  Vi»cit  reftittitioh^tn  stbcirisin* 
leirioi  is  \  pbteruht  igifcut  «^orpbrA  iil  tctrain  dctab]; 
i|t.  N.  A^  Quahtum  <t\itn'triril1tn  <*o/pori  dd  defcei^d' 
fiiih tribuituf  per  «rhcr«;m  debirfutn  ^xcarlfeiiteth,  kanl' 
iqhdcih  virlutn  ittifcrrtir  pcr  srthc^Cth  inferiDrtih  fiiSf 
leilLtUchttfhi ,  cuiii  In  elaftidi  Vii^  refticutionis  Ad*t[ue| 
Viin  cohiprcflldni).       Jh  Quid  (i  honiiutiqiiim  in  co$n 

?'>u$  gravc  pt^ius  agdt  letbcr  iilfcrior  (c  relhtuchS}  qUani 
upcridr  dcdi^fum  pirocurrens  ((jtibd  ficri  utiqu^  ptP 
icfl^  ctam  i6riid<(m  vibratiouc^  Iiaheri  Btbeaht  (urfumi 
tiuoc  dcoffitm  )  ?  ah  hbn  cbhpus  fbrflirh  pbtiu^  mbVcn* 
dufhcft,  qiiarti  debtfom?  Ditei  IL  Uhdularionii 
^us  aqtiaruth  ftpe  eorjibti  Jnnatanti&  dd  littu^  'cjt2 
ciunfur;  quid  hi  etlaiii  dlcillatiahlbtis  ^thereii^  ddrpo'-' 
H  detradi  pdfliiit  W  tcl^ram  ?  %  i^i  C;  Mdltbhl 
difpar  eft  ratid  iinduUtidiuiih  ih  aqtta,  fk  blSilliltio^L 
hum  in  ^thcrd^  Sit  (.fyt  ^4.)  lihca  hdriiohtalis  A 
i  dcflgnanH  acJtilHl  traHquillami  thciimbat  ^aqb^  Veh^ 
tus  iti  €i  ica  uc  ibi  iqui  d^pi^imatar  ;  titSttff^  ^ti\  dint 
itm  attbili  in  D ;  binc  jjrelro  dclabchik  rurfus  ciaVitAtettl 
tfficlet  itl  E^  eoqae  ip(b  hirfuii)  aqua  lalforgct  ih  f 
rdapfura  fiartim  ili  £  j^artim  lii  O^  &  iit^  dcihcepi 
alccrtti  crUac  a^aairum  a(ecAfd$^  &,  deAlihibs^  ^m 
«ndJr  prDJ^ugentdit  id  $fdHi  iit^s:      1?6iH  )knimm 

t  i  •        Vcf- 


^fflBt  litCM  wnuKmpi  cflt  dcbcc  coiiciulniiii  «ccn* 
fliciiciim  firc  cx  cohslionc  iivc  cx  «ffndu  nataiii  (  his 
tsiin  dc-  ccolGf  fcoipcr  cliqaUI  iinpctiic  aqns  lcbcmis 
ci  Din  £,  vcl  cx  Fin  G  amirrimr);  hinc  miaor 
cfl  ioipctiis  cqox  aiccndcntis  cx  £  in  F,  qnam  qi»  pra» 
ximc  dc(ccndcrat  cx  D  in  £;  qaoctrcc  ftmpcr  plnc 
cqu»  ddabitor  «x  D  in  £  ^  qoatn  rclabctor  cx  1>  ia 
C;  qoid  jammirom,  fi  pr»ralcmibos  aqois,  quaruin 
IfttXUi  cft  ftfCag  lictona,  codcm  corpoc  dcfcrator.  -  Ac 
fcro  poirui  matcric  claftic«  infcrioris  «qoaics  (bnt 
polfibus  matcric  {operioris;  crgo  squalibus  oppofitis 
viribos  lc  fk  clidcoUbus  quic(cct  corpus.  Dices  117 
Vodsi  tSrcir  pcr  campanarum  pnlfus  ,  ac  tormcnto- 
rum  cxplofioncc  cxcitacx  morcnt  nobcs  ca!T>  in  par- 
Cem^  vcrios  qoam  fiunt;  fimiUtcr  &  ribrttioncs  a^thcA 
ttm  mmrcrc  potcrnnt  corpora  vcrfiis  tcrram.  ^  T« 
A«  Nnbcc  cniib  fulminibns  f(£t«  rcmotioret  iUs  qui* 
4fnii  movcniort  non  viciniorcSg  quse  intra  circnlos 
^Aum  ac  vibrationnm  conlUtut^  rompuntur  potioSp 
A  quafi  convcliontur.  Scd  T.  A.  N.  C  Non  vi« 
brationum  in  acrc  cxcitatarum  ,  (cd  ventwum  opt  dc«^. 
fcruntur  nubcs  rcmotiorcs  cam  in  partcm ,  in  qna 
polfiis  fum  aur  oronino  nulli,  aut  pcrquam  cxigai; 
liam  cum  vibrsribncs  polfii  campanarum,  aut  cxplo- 
fionc  tormcntorom  gcncrat»  ad  mt}ua  fpartuni  pcrcin. 
(ant  ^  in  qao  a&ris  rariorts ,  &  dcnfioris  viciflitndincs 
babcntur  ^  comquc  a&r  lafcralts  magno  impcru  ruat  in 
rariorem  ^  vcnros  oriri  ncccfle  cft ,  qui  fluxu  fuo  con- 
tlnuo  nubes  depcHunt* 

^f  i6g.  Cmffk  ffraviutis  (^parum  urrefiri^ 
M$  ijt  sttraiiio  Urr^  agcns  ftcunium  Uffs  ixpoftoi^ 
cumprimis  inratiom  ricipnca  dupliCi^ta  difioHtiai^ 
rum  majdrum.  Pr«  lllud  dicf  debct  cauffii 
gravitacis ,  per  qtiod  rite  enpofiunttir  ornnin 
pbsnomena  gravitatis}  ar^tti}  ttgo^  P«  ni« 
^  Prac* 


c 


Di  mtu  ffrgvium.  fk^^ 

% 

Fr«cipua  inter  phaenomena  graviiratis  habeii* 

tur  fiKjQintia :  I.  GravtM  liberc  defccndentU  p^ 
runtur  in  /iiperjrciem  terr^  Uncis  ad  fenfum  perpen^ 
diculmiiui  (re  vera  enim  ferri  QhUqtif  docetn^r 
exemplo  lapidis^  e  malo  demilli  )•  ExpofitUi 
Terra  ^finfum  fphxrica  eft ;  und  fic  corpo- 
n  trahit,  quaii  omnis  ejus  materia  in  centrb 
•olle^a  foret.  Cadat  jam  corpus  in  quodr 
Mnque  pun^um  rphicrae»  vel»  fi  dicere  U* 
jCet»  circuli :  cadet  in  tangentem  ,  cum  pelr 
quodvis  curvirpundum  duci  podie  tanger^ 
Atqui  reda'qu£vis  a  corpore  extra  circuldfh 
))omo  du(5l;a  per  centram  circuli  eft  ad  ta^ 
>entem  in  pqndo  contaAus  perpehdiculv 
is»  non  minus,  quam  ea»  quat  a  centro  dgh 
Cicur  ad  peripheria?  pundtum ,  per  quod  ag&^ 
tiir  tangens  (lfefcif//;ft,  3.  propof  ig. );  ««"gP 
IL  Gravh  o^nia  tendunifi^ififiliter  Unea  feBa  a^ 
c^ntrum  teUurif,  Expbf.  Gravta  linea  perpen- 
dicuiari  feruntur  ad  taogentem »  five  (uper* 
flei^m  terrx;  atqui  eaaem  perpendtcQlaris 
produda  tranfit  per  centrum  {phirx  (pef 
Ceom.)  ergo.  Dixt  fenJibiUter  nam  in  rigorc^ 
tflirer  A  res  habet;  fcilfcet:  terra  cum  exa- 
Ae  (phffka  non  fit ,  M  rphaeroidica »  ad 
(j^haerani  tamen  proxime  accedens  ^  gravia 
n6n  omnli  r$  ipfa  ad  terras  centrum  tend  anr, 
ftd  ea  distiraxat  ^  qu«  fub  polis ,  aut  (ub 
iA)uat6ro  cphftituuntur  ji  aliorum  diredia-de* 
fieAitacetitro  terr«»  plus,  minusve,  prout 
magis  I  *  mihus ve  diftant  a  polisi  vel  ab  irqua- 
tore •      &#m  ocuiis  fub  ficio  in  fi.  %%.      Sit 

T   j  ^  el. 


flliDfi^  D.4EB  refercns  rerr^m;  qatot  ^mA 
(int  in  eyrremiraribus  axis  minoris  ^fii  (Hin« 
^a  rer<>  «quatoris  fint  in  extreipicacibus  oi^ 
Joris  ^xis  £)  E.  Corpus  in  urroYis  pQlorum  ^ 
Tel  ij ,  irem  in  nrrov}s  pMn(;:)Q  ^qqacoris  conr 
flfiriirum  5»rcrahitur  lanrundeip  ^in  parteoi 
nnaiTit  qiianrum  in  ^ilrer^rn  j^  rum  Qh.asqtuic 
leni  nam?runi  p^rriuoi.  binc,&  ininjf  rrahcq^ 
flupi,  rqm  ob  xqu^letn  parrjum  urrinqueDn^ 
$rariim  djftanriwn  9  forpprf  aitrah^nd^ 
Q^^r?  Rcf  linfjim  intermc^ian»  m\  cjebct  in  y 

dL     CpnnitqatMr  jam  corpus  in  pun^^f  Af  j 

|i|Qq  tend^c  acj  cf ntri|m ,  quoij  Qilendo :  Rair 
€iq  Q4  ^crcriba^ur  circ^lMS  refer?n*  fpha:^ 
f^m  fRli^rQi^i  infqriprain ,   tr4(l^(ar  ?Qrpu| 

11  nQo  niQdq  a  fph^r#  inrcrip,r?>.  ffc!  parncf 

tb  ^xc^/Tm  matcri^  fphajrfiai^pf  Af  |J^(?,  ^ 

mENEx     Im^^  ^phxr*  fpUMs  attr^^ia  a4 

<P?ntrqm  rendic  (^cMndufn  dire^ioneni  linfii 

^C^i  rfraaiQ  ^ur^m  xefulr^ns  ei(i  atiriK^iQt 

IjihMS  cJi^prMm  C wfflmnpi  r^nd^ff  ^^feetprot 
P5  .il'M<l  cenrru.m  in  RqnaMm  «liqqo^  |f  vi^ 
fJniq^  puq^a.Xf^^uam^i  ^trrjiaiQOfSi  cciirii 

jttn  r«HMn  apOim^nrnr  «  malB^  tr^hfnubu% 

(qux  hrc  |f^ii^(es  fm^t)  fed  ^rwm A l?cipr0e 
^a  duplic^ra  cli(^anria(  qqar^  tjwQi  fH<?^(rm 
MP.%<y  vi^inipr  fir  (fQrpQti  ^,  ^t|ra^^a  fJHi- 

ra  4.§f  .^  ?»her-fMri  feqM««rfrscv«Jireai(k. 


t 
.* 


Jlr  mwi  gtmAmu  \        W9% 


wmi«   :  UMinqoa  tamen  NNfta  illa  non  <!?• 
'Cig^cur  tti  camrumi  iidhac  tamen  ad  tangeh-' 
vf^mperpendicularis  efle  potefl;,  btnc  adbuc 
graTia  in  fuperficiem  ^h«roidis  detabi  po& 
-fiint  linea  perpendicularu      IIL   Gr$via  libcf^e 
jffifunJcHtiM  fmtu  umformiier  accclirato  fcruntur  in 
^crrsm ;  furfum  projcSa  motu  uniformitcr  rct/crJ^ 
^o.abcunta  tcrrs.      Exjpojkio:  Gravitas  in  mind* 
ribus  dtftamUc  ^  in  qoibus  vulgo  eicf>erfmenti 
capinius,  tft  vis  acceleratriK  eonftans  (§•  l6r. 
A£cru  VIII. )  {  ergo  ejus  u&\o  in  corpiis  five! 
xlefcendens,  fivea(cendens  motum  unifofmi- 
«sr  acceierare,  aut  retardare  debet.      Nihil 
^ztn  mirum^  fi  gravibus  t erreftribus  ^^^f /u- 
^oi^ficicm  urf4c  coQftittttis  applicari  pofiunt  ee 
^Mrnia,  quas  ad  motom  uniformiter  acc^lera* 
<mk^  auc  reeardtcum  dl(fta  funt  in  Atccbamca. 
vlV.  Ex  ff^mritau  namm  paudui  cfi  accuratc  ntapc 
imra£Ut  frhportionalc  {  mn  m  men  gravitac^  q  uis 
CeRiper  eft  inr  ratioiM  direAa  Ihaflarum  tra^ 
4mtmm^  8c  reciproca  anraHarum^).    Bxpof.  Pon«> 
lios;  quod  Hcwmna  dicitur  vts  motriXf  aliud 
iipn  ou ,  qgam  echricas »  hi c  gravitat  mu!tiplU> 
umpcr  maffcmi  ftal  eft  vts  acceleratrix  lotitfs 
fiin^pta»  quoc  flint  particulas«  minimae  mcX'* 
fam  aliqnam  componentes  (  ubi  iupponi  de« 
bet-omnes  particfilas  minimasinvicem  lequa- 
\u%  etTe);  >ergo  com  marveme  eadem  mafia 
trabente  qtuevtt  oorpora  in  paribus  a  cctitra 
terrardiftantiiaiocata  ad  «qualem  eeleritatem 
determinenttir,  debent  pondera  efre,  in  ratio* 
W  dire^  mmctmn  attra^um^  cenrequemer 

T  4  «Ptf; 


< 


1 


i^         Sttlktt,  Qfmt% 

m^  proporUdnaiiA,  AMlytiet  fic  npmi^ 
b«rist  eft  P^  MC9  icp  :si  m$i  ergoP  i^ 
mMCx  mp.  Et  quU  Css  #,  btbecur  P  t  p 
mMt  m*  Vf  Gr/»ir4  terrtJhrU  in  miH^  mm 
f(i0$9$9  C3(  (Adm  4kitHJm  dtUk^niia  mfnsH  ##* 
HriW4  firnntHT  pfrfm  wirnm  t^rr^»  ^^f9fi 
A^  certini  vtlecuarem  corpora.  ^eiermtnoQ» 
tur  roluin  II  mafpi  tmhente  {pmihm  d^4ntH$  ){ 
|l«e  vero  cnm  eadtm  fi?  rdace  j^d  qu«vis  cof^ 
pore^i  eademqae  fatione  trahatcorpore  es 
tjidem  «Ititttaine  demiflli  (  nimirum  pro  ti^ 
tione  molecularum  rerrem  eonfticuenctuRi ) 
ibqtit  debec  in  mtdi4  mn  rt/^mt  «quaii^  d#» 
icen(ii$  omninm  eerpofiiiii  ab  eedm  cerro 
•qualicer  diftatttiam «  urcanque^  tadem  inefr 
£9  9  aut  volaminibus  difcreptnt»  <  Mh  h 
diQ  rp/lfiente  mp^rs  d$t^4m430i.^it4t4f$ 
tnr  vtrfm  ttrr^m^  ^nnm  pnritrn  i^44tttrU  Pm^tii 
diftanci^  rcilieet»  ec  vdqmino),  S^  Ctt^ 
porii  enim  nonniii  finpdnntm  tn^km^irmttl  t 
quibas  coalercunt,  vi  af  e^fdor  fiiperert  H^ 
tuniar  reGfi^nTiam  medii}  ergo  qufi  meftf 
fueric  molecnUrum  eorpui  qM^vis  eonftt* 
tutiuiam  numerus,  hoe  ^rit  ma|or  oerandefii 
Tis|  proinde  facjiius  fuperebltw  medium  r«# 
iildnsama^a  denflore»  ^fuem mriore,  VII« 
h  ^Pt^Hf  fiikttrrmui  %  fid  ifos^nndi^riht  min^r 
ifilfQrtmrnm  ^r^dtm $  fmm  in  fiftrfiat  ttrr^ 
JfiMl?  Univerfe  enim  a^treAkmei  dnemm 
ibMrarum  fanc  in  rattQHt  dif e^e  radiorumi 

M 

ftttilieait;ri  tmnis  taifflactca^la^--p 


H»  ifiilif  grtQim^  t^^ 

ilf  • 

MTtro in  (>b«rb «iP^Se X)  s»  11$  trgo  — ^ 

»5  '^"x^:;?  /l  \    Afqist  ftiinor  eft  rddit»  *  coiw 

tro  terrar  duAas  ad  profiindatii  fi^cuni  fub* 
torraneam ,  quam  ad  fuperficiem  tittsdero  toN 
r«  j  ergo  fimUicer  minor  eft  afcrt^io  tecritj 
Con(equenrer  8c  gravitas«     Vlil.  Attr^Qi^  ff 

f^f^f  Otraque  e(t  rh  cominuo  «^irin;  motui 
igitur,  ant  (juies  maffir  five  trahentis,  Ccxi  tra- 
hend^  n}Wl  confert  ad  effci^um*  Qfi«  re» 
liQua  fuht  pbxnomena ,  facile  exponuntur} 

fea  mentem  Tedulo  advertero  oporfet  ad  ea^ 
^u«  aliat  dixif 

SM*  l  Sqperac  objc<U ,  foramipe  ibfiifioiiei 
ffteit9re«    P Ao  «triimqiie ;  ^^Stlmftire^  ifwi^nxm^  * 

M^etfas  jf,  tfi}.  Oppwhtfr  f.  Sji  datwr  itiutna', 
ee  oniirertiilis  eorperQfn  wraiiio  ,  corpora  omnte  in 
ae^rytim  tinam  coire  debebunl ;  non  titi^em  eo^nnt ; 
ergot  ^r.  M,  Omnia  T^  fc  mqtdo  frtheDt ,  niutaoqqe 
4^tepmimiNYit  ad  acceffum  j  ergo,  9$.  Ni  Seq.  M; 
Ai  Pr,  o  Ai  Omola  ft  mqt t|o  tmlienf  prepe  inmR- 
kilitw ,  fimulqQe  traiientqr  validiiCme  ^  tcrra  C,  At 

i^hiibiilter  I  «m«quc  validc,  ac  a  ferra  N,  A-  &  Ct 
Mntiia  attra^io  duarum  (pherarum  (<}Qiiram  dtame^ 

fcr  fitpedts  iiniqa,  diftanfia  pednm  ip.)  el^a^  wn* 
#ionf»m  terr^  relatam  cd  eat^em  fphiBras,  ut  i  i4 
Ifj^^ptnoo;  ergo  propc  infen{]biUt.  Hhic  fph«ri^ 
jliap,  «4/^1/^  amui imp€4imnkf^ t  yi  fi>tiuf  |raeitatis  myi» 
fuir  ad(e(e  accederent  ceUriratc  tam  CKtgHCi  ttf^  Utfi 

ftft  lepgi^onin  anoorttin  UttirafcdiSNii  1  nrqoi 


09f  SauM*  Ctfia  n 

nwa»  (ciitiri  viK  poi!et.  At  eniin  liodic  imiltDn 
impecUc  cHlr ;  imfMiour  Ptmya^tie^  j8c  ^mtm  c^ 

iriniies  terrc ;  impedit  (cabrities,  qoc  politifliinis  etiam 
iphxrif  cominiiiiif  cft;  impediant  vires  aliornm  coc* 
jK>nm)  fpioniinv  Qooibo^o  iM|i  cor pora  io,  uanQ» 
nccrvnm  coeam? 

II.  Koti  experimar  mtttnam  attradionem  ;  qnlf 
^eti  patet.^  ^  K.  Nan  experimar  T.  A,  Hcpe  eniin, 
^e  per&pe  fkifiUlem  effe  do^oi  f.  i^«&  14.  Koii 
<xperimQVy  inqnam,  in  moltit ;  at  ratmei«i§  cruimm.' 
tf,^  U.  Conotpfis  a  B^ikovipki^  verbis  1  haftusfmKjh^ 
f w  ijfli»  cmfi^  impngnari  ftffe  gravitattm  nmtunm  gtr 
fttr^lem ;  nt  ejjfft  is,  ^^J$am  ubu  effi  gra^vtm  ceufof 
r^t  idcirco ,  qnod  crajfum  |  V  bcne  ttufiimjuum  uibu 
'^d  finfim  vidirft  defrimi  ipfi  ad  oum  fmtfca  adv^lante^ 

■  Ilf.  'Vel  atrra£^iO  motoa  feniibilis  eft,  vcl  ifl(cn« 
iibilis.  Si  primami  qaidnain  eft,  qaod  iapia  prope 
vaftam  tarrlm  libere  dccidcns  ad  eam  non  accedit  ^ 
ittt  qaod  .pYndoliHPi  non  qnidem  In  moatif  apice 
ciyiftttatiim^  fed  prope  jnontem,  tamen  ad  eam  noft 
ji<pQUnat }  Si  i^cram*  qopmodo  Condafummii  aiiiqoe 
p^ndjKdom  l^tios  o(Viiia{Ic  firront  in  montibos  Pcrtuie 
fiis  ,  q^iim  in  v^iibos  J  Atqni  vcro »  fi  omncs  mor 
lcculif  tiTihfifnti  pouus  vciocior  ofciUatio  futora  fuif 
(k^l  ^o»      V'  ^'^^  v#riis  corporupi  crabcmrum  cifr 

«amilimiiA  iam  («nKbiUs  elt »  jain  inr«nribilis  ittre^io; 

^       ^  M  l 

f  qrn  «nim  ^h  nura^ivii  (cmper  ;?:—-;  pi^o^  vmSEi^ 

filfil  ^  HHI  diftantiaruin.  di&rimen  notabii^  mt ,  Qc  a^ 
^^ior^v(k%     Hoa  gcncratim,     Spooiatim  vcro  ad  l%i 

Ei^pm  ppll«  Ya^ain  turcim  oidcmcm  qaoJ  facit,    1||. 
M>i^  H(l.  W^i^  acQcdcr^  dcbcrct  ^  nifi  attraaio  tir- 
r^s  l»(;^Q  9iMMr  cd^:^  quaoi  qtmp  lentiri  polQc  relatf 


^f  Af  Ct    Str  licet  vls  4ttr8Qiy«  tvm%  t9»ia  %  qu^nty 

^lobi  ejusdem  cum  liitri  denfir^tts^  habencis  iXzmt* 
frurn  5«  pijfTuqm,  feii  40.  ped^  G^omf,   tam^n  attra<9 
ftio  tMxf\%9A  iHam  terrs  fric  uc  1  «4  lopoeoo   (e{l( 
^nim  ^o;  40000006  =;    l  :  xpOQOOp;   yidt  f.  r6rf 
^f-^h  VIL).      Pendulum  prope  ipontem  infignitf? 
Vaihvni  nqn  decltnare ,  pr^fraSe  nego ;  t^ftihus  eniiA 
Af  ronQmis  Galljs  pendul^m  pfope  montcm  Cbitnb^^ 
r^4^  %lferticaii  ruudeclinavit  7.  minutis  (ccundts ;  qu^ 
c^fCliAatiQ  cutn  exigut  f^erit  refpf^dii  monris  iil2t\s  ad^- 
fnodpiv  xngentis,  meritO  fufpic^ri  licet  di^um  nton. 
j|fefi|  cavum  efTe  |  &  cru(|a  cj^u^dam  per  ignes  (l^bterrai? 
1190$  elevata  coniUre,   quovum  (juidem  i^nium  plorif 
|na  xllic  l^bcnu^r  indicia,       Sedi    cyr  pendulf   jjuxtf 
l^ontem  eKC<;lfum  poiita  nan  paflin]  declipant  ?     Z}i* 
€W^t  $spc  viclni  montes  a^trs^tone  proprU  in^pediunt^ 
^spe  minor  eft  denflias  montls,   qnam  fieliqu^  terras^ 
$spe  ii^ont|um  pyraipidalis  frgursi  officit  ^c*    Quo4 
fliverfis  penduli   o(ciilantis  celeritates ,    in   i)nont|bu| 
|Vn!f4lf/i^  Sc  v^Ut^QS  npcatas  atcinetj  ajo  diyerfas  no« 
f^ri  deboifTe ,  quamyis  diverfitas  m>\\  refppndcrit  ra^ 
4(oiii  dhreB<^  maffarum^  fcd  ^otius  recfproc^  4^pl^at$' 
^iOantiarum.     In  caufll  efl,^  quod  hon  ta^cum  lit  at* 
tra^ionls  incremencum  tx  p'e(c^i^te  u^afTa  ^ .  qviantumi 
%ft  decrementnm  ex  anda  (li(lanti^;(  §  163.  fpJ!tioni$ 
^artc  11. )«       {ter^m  patet ,  cur  in  mbintii>us  iioftrts^ 
^tiorum  ahitnd»  wtaiilis  ^on  ffi  rehte  ^d  radium  teT^ 
ftflrtm^  ^i^vifatif  divc^tas  poft  a^verti^turt 

ly.  Si  datur  fttra^i(i't9UCQ«  (^qi)e  J^n€bi]rf|' 
^lPpHes  corpus  actrahens,  omnino  vafinni  eft)  6eri  p^*!'; 
^c  <|ebct ,  ut  ad  prxfenti^tiY  Lu^^*  miciu^t^r  cprpo, 
fQq[i  tcrref^rium  gravitaa  in  terram  X  partem  ^niq| 
iprayitatit  (ibl  venlic^hit  LuQa).  Not»  avi|cm  ^pj- 
fi^itur  ,•  ergo.  |f .  N,  Seq,  DQ^uit  Ne^mM  if  }t 
frifieip.  frofef.  if.  A*^t  %•  W^.  Lvmag  £|iu»x  ftQfa^ 


^oo  SiSlhlL  Cdput  VI. 

Co  dicitli )  non  id  proeadcndos  effeSns  tltos  ;  unae 
ttalla  vis  Innaris  ^dvertitor  in  expcrimentis  pendnlo- 
imm ,  vel  (lacicis ,  vel  hydrollaticis.       Cl.  Eulerus  d<:- 
iBonftravit:    jdiflTerentiam  in  ofcUIationibus    pendulo- 
rnm ,  dam  per  ^dionem  A/iV ,  6c  Lm^  gravitas  ina^ 
%\mt  augetur,  vel   minuttur,    cam  dnntakat  haberi 
poflTCi   quas    intcrcedit   inter  ilnmeros   4666666  ^   C$c 
4666667^       Qnis  inde  gravitatcm  diver&Ai  arguat^ 
welebcrrifTu  commentatores  in  Nemouum^   PP.  ^ac- 
fuier  ^  &  le  Sfur  ajunt.t  quemadtnodom   (i  granuni 
unum  comparetur  cum  pondere  4000*   granorum  ia 
libra  quamcunque    cxada,   pondus  grani  iilins  hand 
{entitnr  \  6c  vis  Solis ,  &  Luna  comparata    cum,  V| 
gravitjitis  in  terram  (cntiri  neuttquam  poteft ;  eft  cniuji 
§t  immenfam  diftwtiam  (umma  viriqm  SoliS)  &  Xu- 
nz  ad  vim  gravitatis^terreftris  ^  ut  i,  ad  %Q%%%f^p. 

y»  Tanta  fl  cft  eorporum  terreftrium  vis  gravi* 
tatii  in  t^pratn,  nulUim  partialc  corpus  corpori  ^dh«r 
rerc  poterir  \  non  puIvifcuU ,  non  gutt»  aqu6s  fpcqti^^ 
'  }u  verticalitcr  pofito,      Contrarinm  cKperimur^  ergo^ 
l^.  O»  M.  Nifi  gutta  aqus,  aut  pulvifcqU  a  quibus* 
i^nnqu9  eaultis  esctbrnis  ad  fpcculum  appUcentur  in  tan^ 
niihutif  diftantiis,  qt  {enfibiliter  illqd  condngant  Ct 
M*  id  d  (W  N.  M.  C,  m,  &  N.  C,     Ad  hjrc  fal. 
Mt  objcQioj  ponit  enim  atrraftioncmiii  adm^iume^h' 
gnift  Si  if^fiu0iliit4s  difl^nmt  (igerq  fro  rmhm  4^rf^^ 
fi<I  f^^(9rnm ,  6f  rfciproca  dvflicata  difiantiarwh^  quod' 
apiFCfi  iiificiaamr.       Oi^tingucndum  nempi  oft.inter 
irrra^iionca  illas»  quas  deiignat  curva  axcm  in  minii^ 
mii  diftanriia  idcntidem  interrecans,  ab  attraebton? ,, 
^«wni  exhibct  ejusdem  cqrv«  cruis  altcrum  TpJ?^»^ 
lu^iorvnn  attraSkmum  auantitas  non  pendet  a  quadra^- 
to  diftiniit  inverA^»    Aid  a  divagatione  arcuum,  tn^ 
%m\^iAnp  ordinatarum,  ^  a  diverfa  virinm  compo(i« 
Ran?  ,  h«C  vero  pol^crior  ftquitur  legem  illam  woi» 
vtfialem  tfe  t ar jonc  rtciprQca  4upliwi  diftanttarum  1 

^wa* 


I  \ 


ad  Q)ecult)m  babetqi  attidem  per  atti^aflicmcm  ^  Cti 
0gefit€m  in  fmiimis  diflamiis  ^  qux  non  (equitur  di« 
oam  leeem ,  ad  difbifitifls  (blam  majores  pertinenteni, 
Dicest  n  variatis  diftantiis  variat  lex  attra£lionis,  d^ 
plicis  gelieris  adftruitor  attraflior  prp  miwmis  akera» 
alccrapy^oi/^a/oW^xdidantiis.  9.  N.  Seq.  IdemplanK 
ignis  in  majoribus  diftaniiis  calefacit  (blum ,  &  iila- 
Qiinati  in  minoribus  etiam  inflainmat,  &  comburity 
nequc  umcn  duplex  audic  ^  ergo  a  pari. 

VL  Si  caufTa  mutu«  attradionis  (peculo  vertioa- 
Uter  pofito  adhxrct  gutu  aqus;  quid  non  granttm(a» 
buli,  aut  papaveris ,  qua;  &  pondere .  &  voiumint  ma» 
jora  funt,  quaro  gutta  aqiic«  ^.  Guttam  inter  aque» 
am ,  &  granum  aren^r »  vel  papaverit  multum  incereft|. 
fphsrnlc  minimc  ilotaorum  g!abr«  fiint|  6(  conccn* 
tricae ,  facillimaqoe  ali«  circa  alias  revolvuntor »  deni* 
que  ob  mutuam  attrattionem  continuo  ad  «quilibrica» 
tem  (e  componunt;  bitic  quantumvis  paucK  fluidorttoi 
molecul2  (pcculum  ph^ec  contingant«j  jam  tcliquai 
poft  (e  trahunt,  fpecttioque  adhsrent  cmi|es  (  quam* 
diu  adhxfionem ,  aut  cohcrenttam  tion  viiicit  pondol» 
fiipartium  vinculanon  di(rumpit;  (eut  quainditteon*  / 
cre(centes  gottul«  )u(tam  aHquatti/magnitudinem  ncit  . 
adipiCcuntur  )*  Ac  papaveris,  vcl  afenic  grana  a^erac 
babent  (bperfictes;  qtiamobrem  tn  paoeia  admodttm 
pttnfiis  (peculam  centingunfi  &i  quod  nltro  ccnds* 
qttitui^ »  eo^um  attraSionem  facile  fuperar  potidoa  rc» 
liquarom  partium  (etilibiiicer  diflafttiom. 

VlL  Si  mtttoe  (c  trahtmt  omnia  ^  mntnc  qtioqitc 
accedent  omtiia.  Accedenc  itaquc  Soi»  &  luna^ 
fttin  pianet«  omnes  ad  lapidcm  |  fcrta  lp(a  terfiia  aco« 
mttm  aliquam  in  ultima  ai^ris  rtfgione  volitantenl  a(^ 
fu8]|Ct«       ^.  Acccdenl;  aCquc  dc  koc  t^ilii^»  qui 

tiiw$mm^  B^ikmchkm^  9^  frind|^aa  alios  hodierni 

(ai 


fHt  mitiffime  (criblim  )  fibcali  Pbflofo^W  fe^nildr^ 
«ubiaoi  tff^  pot^ft*  Ac^edtnti  in^tilim,  liAtiiadj  ^na»^ 
thAte  mctas  ^oUbH  ,  at  itt^auali  ukriiAtt  f.  IV.  Scbol^ 
IV.  V.  &  Vl- 

VltL .  In  hy|>othe(i  AttniAIotiis  mwtwx  tfthettt^ 
coqMU  qbodlibct  a  qaibosltbcc  ailis  corporibas ;  ergo 
ad  fingala  acccdct  eodem  ttitipore  ^  &  motibus  oppo« 
fids,  «piod  rcpughan  Ify^  K.  C.  Attrailioflei  xquaA 
let  &  oppofitas  primam  kCt  aildentf  tum  ciirpasat^' 
tra&um  fcretur  motu  compofito  (vi^r  ^.96.  ScbuL  IV)* 

IX«  In  «adcm  hypotheti  eoi^porum  oititiium  figu^' 
fa  (phcrica  aflfc  dcbctet  1  prol^fus  ut  corpbrum  qoo* 
rumvis  totaliam ,  aut  fluidoram  in  guttd^  (ccrctOrumi 
Spbsroica  aotem  non  cft ;  afgo^  -  Fr.  Sdqi\.  M«  Oot<- 
tz  fliiidortim  ipfasrriCte  (bftt  ob  itlutudm  attrafllonem^ 
&  ffqoiiibrlom  \  eigo  iisdem  de  Ciiuifll  cm-pora  qosvis 
Iphxrica  efle  debctctit.  l^.  Corporum  omnium  figa» 
ta  rph±rica  efle  deberet ,  ii  extr^neordili  corpordm  ac*» 
traaiottCi  nibil  turbarent,  dam  corpota  cSt  ftatn  flili* 
^itatis  trtnicnht  irt  (bitom  fbliditatis ;  item  i  fi  OmnCs 
molectii«  minimc  figura  (atis  labrica  inilroftft  forent 
C.  M.  p«ftqaam  five  attradioneS  estrinfecar  idfaiitfi 
iive  corporaiam  obtinaertiilC  ftatom  foItdifatiSj  (ea 
licniqae  noft  omnes  motecalde  mininic  figura  (atis  gla^» 
bra  inlhfoa*  ftm  N.  M.  C.  m.  &  N.  C.  "  Si  partlca* 
Iflt  minimft  corpojrum  ab  ipfb  (ai  eicdidto  flguram  (a^ 
fif  Itibrlcam  ObtinuiiTetit ,  nqae  extrsftes  virei^  matctam 
carandem  attradioncmtiihii  ttirbafltilt,  corporom  omi 
l^iom  figura  fbcara  faiflfct  fplMtrica.  Cum  vcro  iputoa 
mioimaifam  molecolartim  attfiifKo  f^er  extt^infeMs  aliOw 
rnm  corporam  viteaimpedianir,  cumque  tcrum  cbm* 
])ofitacttm  mo!e(^ulse  ctrtas  qaaspilm  figutal  ib  ipfa  ha* 
tara  itiditasobtiboednt;  tierl  deb^at,  itt  in  limiftbtmt^ 
ad  qaos  ptimum  ddfcrentor,  c^h^eretit.    Dica.  Mti^ 

licolii  mifttmii  iercaa  %umi  Hatme  tkiUii  Itiditit 

•ffe 


/ 

f 


Ae  cotnmemuni  eft.      ]$•  Sit  maniftde  rcritttcm* 
ofteiidit  fliccefiiva  corporum  gcncfis  cx  concVctione* 

Schol.  IL  Ad  f.  167.  prster  ea,  quxibidemre* 
citavi ,  opponi  poflfant  feqiientia  :  1.  mancnte  eadettt 
mafla ,  &  variata  dnntaxat  figura ,  mutatur  corporuot 
gravitas  ;  atqui  routari  non  poflei,  nifi  cauflla  gravi- 
catis  repeteretur  ab  impu]fione  fluidi  cujuspiim  extra* 
nei;  ergo.  Minor  Cartefianis  ccrta  eft,  nam  fi  cor» 
poris  gravitas  repetatur  ab  attraAione  terrx  (  yuni 
ifii)t  corpornm  omnium  quavis  figura  przditorum 
eadem  eflfe  debct  gravitas,  cum  manente  cadem'caii(& 
iidem  efle  debeant  eflTefius ,  proinde  nunquam  grari- 
tas  mutari  poflet.  Mutari  autem  fic  probant:  vaftio- 
ri  vitro  inetallum  eontinenti  indratur  minus  aliud  cum 
menftruo ;  &  vaftios  iliud  probe  claudatur.  Tum  Q 
ritra  ambo  invcrtentur,  djnbrvetnr  metallnm;  fada- 
que  diftbhittone  comperies  imminutum  fnifle  pondus; 
proinde  &  gravitatem.  Unde  vero  iftud  ?  fi  non  ct 
eo,  quod  moleculc  difllblAtz  intra  poros  menftrui  (t 
feabdanty  obtentoqne  minore  volumine  minos  pa- 
reant  polfibus  materist  pretneiitis*  11.  Idem  fit  de 
g^'pfi  >  &  aqna ;  h«e  enf m  fi  coqimifceantur ,  deficit 
pondus,  Ron  mafla.  III.  fhmktm  vafe  vitreo  her- 
inetict  condorum  ^  &  ItntU  6pe  caUinatum  plus  pon- 
derat ,  quantamvis  nihtl  maflTse  adjiciatar^  Nunquid 
non  iterum  a  premente  ftuido  extrinfeco  ifthsc  repe« 
tenda  ?  gypfi  enim  voiumtn  minuitnr  ^  hine  minus  prc« 
niit  floidnm  incnmbens ;  augetnr  volnmen  plumii^  binc 
premitnr  magis.  Ita  objeAantes  Cartefiauos  indude 
Redlbammis  nofter«  Ex  eodem  Aufiore  folotioneiit 
imelligamDs«  l^.  Manente  eadem  mafla  mtttattxr  gni' 
iritaa  ipedfica  C.  M.  alfohta  N»  M.  fic  D.  m. ,  &  N. 
C.  Abfihta  gravitas  dicitnr  fumma  moktulamm  dm* 
nium  corpns  eonftituifttiiim ,  qualccunque  fit  corporis  V«* 
lnmen*  Specifica  eft ,  quam  corpora  okiiti^tfub  ctr* 
S0  valumine  (4.  6i.)i  ptftet  inde  prjotM  iiiam  to** 

-•     ■  varia- 


flkdtta  lotflt  rirfiri  iiM  pofl« ;  piOerior  trartati  fttoA 
roluiDtnc  varu  eft;  cQmqtic  volamint  majori  reQKHW 
dcit  major  quuirf tat  bt^iieH^  fluiii ,  debet  ctdeoi 
inaflt  anfto  voluminc,  &  ^rv  /lArrt  lentmferri  vcr« 
fiii  cerram ,  qoam  volamine  concrtfla  Ubi  ttmca 
c2r  nibil  impedit  (  quod  iit  in  vtciio  BoyUau^  )  ctdeat 
celcritare  dcJabontor  corport  omnit «  qoamcanqao  fi» 
gnram  indactint.  Quomodo  jtm  Carttfiaui  tb  m» 
«quali  prcflione  sthcris  «qnalcm  (m  vaat^)  corpo* 
fom  qaorumvig  celcritatem  rcpctcnt?  Hic  cnimvero 
maitum  laboratic*  Nec  minos  in  co,  qiu)d  &reri 
tdigancor  majorcm  foknHis  iliius  Jbtidi  fui  portionem 
bodie  ctofltm  cflc  gravitatis  majorit,  crta  minoris* 
pruo  iAud  occafionc  recitatx  obicdtontt.  (^tisrobo* 
dic:  corgypfi,  autmetalli  mcnftrtM>  (iio  diffoloti  mi- 
nor  cft  grtvittty  qoam  antc  diflolotionem,,  mamnu^ 
Ut  ipji  ajnta^  priw  majfa}  Dicont:  quia  .niolecoUt 
diflblucis  itnrt  poros  menftrai  itttttntibot  Cideoqat 
^unto  minort  v^Iumitti )  maiia  minut  pttet  id^bot  tno» 
tcris  grtvificar.  Quaertm  jieram:  Mr  globus  vitrtnt 
tqot  plcnus ,  &  in  alia  flnrvciirt  tqtia  rtreft£iot  mintit 
pondcrtr,  quam  nonrtrcft^lat?  Rcddait  (  qaod  rcd* 
didcmnt  tlias  )  qtiit  vitri  &*  a^m  vohmiue  auSo  mafla 
fir  rtrior,  proindc  feccifice  lcvior;  qoafi  dictiK:  t^ 
muta  v^umiui  majort  mtfla  minus  pttec  idibus  mtte- 
M  xthtrttt ,  cum  hcri  tflernerinr  ahent»  miuori  vt» 
tumitii  mafltm  iisdem  palfibus  mfnot  obntixiam  cflc« 
Nngx ,  qnibus  miflis 

Ijr.  td  Expcrt  L  dc  IL  Sivcmcrtlli  menftroofao 
tdmixti ,  five  gypfi  tqua  diflbloti  poudtis  nitnuitur , 
tion  qoldem  mitiWtt  Juptrfidii  caofla,  led  mqffk;  nem« 
pc  igniculi  y  maflTtf  prios  adftridi,  affiifis  fubinde  meok 
Itrois  ciibcrantor  4  &  pcr  vitri  poros  avolant;  binc 
imminutio  poudtris ,  non  gru^itatit^  Abeunt  maflUs 
Igne*  i  (ta  mafliiltt  lucis  ^  ^uarum  plurimas  contineri 
Itt  gypib  nemo  cft  i  qoi  ambigat ;  gypfum  enim  calctm 

Mifiri  dicimtiti  quntqttii  fubtdtin  pafttm  Itptdit 


^p^  m^iK^gmimR;         9^ 


btts^4Atfaig«bfti9iuri  f^lttdcnon  avei«tu  7     Ideaviii <i«i 
mt4%  accciTionc  ignkaiorttvi^qvgi^rarfi  ^f  li«fi^^ 

i^Oi«  .    i       .     «  ; «  '     . '      .    p 

tmam  pocius  ^  c|ttiini  atiani  }iii)iis  onivn^fi  |Nu«im  .tM^ 
lcijra  (ka  Taruntur,  dcorftun  «nota  tk  i^O  jemidi.di»*: 
Wiit  i  aiqul  gravia^omnia  |  dt  6  £b  ioertia  i  ftinat; 
lpfiiiiiivara*nci)U€ui>t«i  4^ut  locum  alio^  pr«  alk^^ 
liMi^4l^urar.|^QtiV0t  3  j^rgo*  Ita  Putcbnm.  q(«/ 
N.  ^*  tion^opos  ab  alio  detrudi^  (ufficit  ab  alio  dttfr*, 
tninati ,  quatitumvis  moyerchtar  vi  tnotrice  tntrin(eea^  ^ 
ilac»r«g|^%pijyin|^^^^«ir  io  ^din,uM^ioi)em'  convci-ter^ 

potc«AISi»4  ^4r i^^ ^^^^'^^^^^^  argumtntooij  gi^VMl? 
•oa9».adideif||Pi)^4f:g(gitMf  at^  ej|ti?inAtf|fivt «  w^^i 

*  #  \p    •       a   *       *  _  tf 

V.  Sxperlcmla^tftt  radil  roUrea  ojW  rptenlt  t*U> 
fticiin  foco  colk^i  dirpefgunt  pulvelres  Antimohii  «0»^ 
4em  ki  fo«o  rtporuos  i  quidoi  itnpuiiio^qr  imveri»  ar» 
tbtrta  fimiliter  poiCint  corporajn  tq?raiii^dttrlidtrcfi 
IHi.  N.  C«  radii  rolaces  non  (iiiitTcauflt  immcdtiij|;a  dj& 
ptffiotlii  fada^  i  fad  aifr  Uitra  pulvtres  iatttaiis»  qut  t  it^ 
Hatis  optradlorum  rolariitm  poris  magno  itnpetu  iHrUtna» 
}itna  pvlyerum  partes  difcerperti^ebet,  ac  ditiicth^  d^ 
ImW  i^^mchtr  nfifttiu  At  dtfceofuia  |;riVium  fie^ 
JrcC  ptP  impulfioti^itt  ir^htns  corpori  incitmbchtik,  fcrf 
jf^M^Hk  ivtfdra  dfBrJhm  Ut^tf^  at  jpHNM^vvir^  IMMM 

VL  &aHe»i  op4  m&hVli  !h  Vdfti^e»  kdft  gHVif 
l|MVii  ctefer^i  p^irunt  iti  tcn«m  i  tkgo»  i^r^  A.  mate^ 
MM  VMrliiditik  ltlerlta$  k^Jb  cxfapcrat  «aUrit^ttin  rerrat 


\ 


smM.a^n 


'SSa 


8  •*! 
■■11  iiNijuic  |PuiuA  cofpon  HOT  Mmm  iiiipviMfv  ^  w 

WgM  «crfilf  tMMk    F^.  A^  cxpcriMiMo  Ck  Nbfc 
JMT i'Vcoww^-fls  «fMIB  cnmnintcr  ■lofCfi  hi  pow 

mi^CVOi  OSCOi  UMPB  fOiOCliCr  COOVCnO  9  *OICOHi^ 

'CBic  ■niiOfMi  kioct  vioi  ccotfifi^poif  cnUfQin  poni^ 
ft  liipcfiorc  -gioK  fcBiiyiif  c^oc  i  Cfgo  c  pcn.  1|k» 
D»  A*  vCKjffi  poiloM  in  iciiini^  non  tcnMn  vtwfiK  cnn» 
S9m§  m^^A.  verfimnbuiS.A.9iC  AdPnN. 
Icqo.  Mbi^  Plr.  dicD  s  MbflM  expciimtntnBi 
jtc  hcbcfc  i  noiqniin  ck  AnSop  iftc  7  oiciiib  fo 

'#  ftfri,  icd  minBtiffiBM  g foMoc,  ili  qB0i  pmt 
ifinn  cnt  otcom ,  mocn  fottMnii 
^kmas  4xi  rf^mUmttm  coU^ 

VII.  Qiric  BM}or  dl  niAt 
IkffA  ,  UgiKim  ih  cqnc  c  flmdB 
dlim*McBr  tx  dppofito  tBijif  <  _. 
v^fOM  UktSam ,  corporc  imptycBtv  diiftei.  ip.  IkiCL 
oJ  eimrum  m$iui ,  ^iB  «iriMr  T.  nondttm  cnim  fihri 
liint  roftfc^f .    «^U  tcBtrmn  r rrra  N.  C 

VnL  S  cqnt  irtic  mocBnqiic  conrcntt  in  dttQm 
ogttnff  portitBte  ccirK  ln4^ioic«  dcfiBranrtir  m4  ffcn^wm 
vmim  i  crgB  fifnilittr  cor{ioni  rortici  iiuictcndi  dcfivri 
po^hmt  Itf  teittrum  ftrra*  Jj^.  nc  ptritciy  quod  cjmit, 
dcndicct ,  infrrcndam  erat  i  ergs  e^rpora  vsrtiti  fooi- 
unsiM  ieftrrt  ptffunt  in  eeuetum  vertieir^  non  itmr; 
qood  tiincn  tibrardam  c  propagni^t  rortictliBi  6^ 
ticccflc  cft ,  qatiqae  cnim  TOrticit  circolot  Xqttctori 
pirciMac  eorpora  dcrnidct  cd  ccntmm  (ttnm  ,  mu 
eerret.  Jj^.  11.  di(p.  in  eo  c(l ,  qaod  in  vcfe  iOocircirii 
Torticii  fint  coneeutriei ;  proinde  corport  hisinntftncii' 
fcrri  p(^nf  im  eentrum  eammmie.  Coticcncrici  noa 
fBnt|vorticci  mkteric  ftbttlit ;  crgB. 

JX. 


'»    I 


^pn dcUiK^cr^riuuff  vfrfm  utarun^  ierfa  ^  ^t dctffodipai^ 
tcriint  •  gcininii  vbrucibut  iti  (cnCuSiwnm^  iMlt  Afap 
gtHiil  crgo.  Fr«  A.  St  ikrctur  %'pm«  onui  cim  li^ 
j(ei9  tcrr^  i£)iis ,  &  idrcr  afai  iMio  |itu|o  tcrrc  «irfitt  «1» 
urum'  flucns ,  m^uric  ^rth^ea  ^  CBrcoi^orft  lerriftrif 
jniuitant ,  acqiiircrcj  dircdtoociii  niCidieiD  |icr  diagOiNlr 
'jbiu  f^crfus  ccnrruin  urr«;  crgo.  ]|t«  N.A.  AdPr» 
]N.  A*.  ycl  cnim  >ortcx  aiccr  altcro  forct  altior,  &  tuoi 
corpuV  dctcriivnarctiir  foium  ab  infcriorc ;  rel  in  oA^ 
^coi  iiipcrticic  concurrercnt  ,  licque  tn  conciirfii  ouif 
luo  iirectio  inutarctur ,  &  rc  ipCi  vortices  defiruereiw 
ttur.   .Pltira  de  voi  t^ictbua  /Vrrair/m,  Franc.  B^^liif  J^ 

3bi  BmnuUiijSif  SamHhI  legca  apod  laodatom  BiflHf 
.   fr^  alioiquc  inultoa. 

tcbol  JIL  M  f,  i6t.  Oppon.  |.  Si  attmaio  eOft 
^cioda  gravitatis%  cjdcin  caufla  divcr&a  ctBiJSim pfOdn^ 
pnn  ^  quod  fV"  tc^ts  fJiwtm  ficri  neqiuli    Pr.  A* 
^uoi  iniin.  raria  corpo>ii  ex  eadcm  altirndine  domifla 
Vaiiiiljccicmafit^uadcfccndant,  cadcm  vii  attra£Hva  in 
iladf^m  diibntiii  divcr(bi   plaiic   cffcdus  operaretur* 
^.  debcrai  cadeio  csiifla  iu  varUf  cirmnjlaniiit  varioa 
,  «flfcdus  produccrc  C.  A.  nn  iuSnn  K.  A.  &  C.    Variv 
f  tia  ctrcumfianttis  vartos  c((c'iarondcm  piuflarom  efc* 
ftui  docet  idem,  ignii  iam  infiainmaiiift  jam  dontaii^l 
taicfacicns.     Huc  quod  ff^t,  advcrtcnda  elt  circom* 
iiantia  non  di(laivti.iruro»  fpi  4^k  n$o$Hw  imp^ditftA  • 
,  y  facilim  ituoidiMoHfm  vHiee^sit  mtff^  waftrit »  qute 
trabitor.    .  DUu  i  fact)it>r  viQoria  impcdientis  fluidi 
in  caufllt  efle  non  vidctor^  quod  corpora  diverfii  celo> 
litatifoui  de&cndaiu  ;  Itcratia  enim  vicibus  eompernais 
eft,  globoa  plvtnimn^  firrtum^^  fftarm^rmm  (  varis 
«loUai  &  pondcrifi)  eg  eadcmr  A^dioc  40»  pedoni 
4ccftdancci  iia  robiedom  aflTerem  f<;vn$i»  iK  ntcaiiriboii 
o^  ocoiia  oihun  eelcntatii  di(criioen  ootari  potocfit» 
y.  ootaii  ooA  poimt  dlCvimoa»  ooiafcleio  $i  bK 

,  U  0  «oi- 


j|oS    .         SfiHo  IT.  Ckput  Vt 

iorpon  impedttio  fliiidt  permodica  cll,  •c^preindc 
Coatcmnenaa  C.  A.  iti«jor  fi  foret ,  naHum  notarctnr 
tticrimen  N.  A.  &  C  ^ 

;     .  . .      '  j, 
*••   '  li*  Si  in  flttraelionem  terr«  refandchdt  cfTcf 

^nflii  gravitatis ,  corpnt  rarius  in  v^9  Bcykano  celc* 
i!us  defcendcre  deberct ,  quam  denfins  cx  cadcm  «Itl^» 
tndine  demiiTum ;  atqui  ifiad  non  f?t ;  efgo.  Prob. 
$c<^.  M.  Corpns  rarins  magis  traheretar  a  terra  i^rg^^* 
Fn  A.  corpns  illad  readione  fcia  minus  viridm  cBm> 
ttft  in  terra  trahente  ,  quam  denfios  ;  crgo  trahcr^mif 
Ibrdns.  Pr«  Ai  ct>rpora  rcagunt  vi  incrtic  Coat*\  In- 
^a  ^utem  proportiQnalis  m  mafb ;  crgo.  Cm^^ 
matkr  z  quo  *  corpus  impulium  ^ft  mrius ,  co  miniit 
refiftit  impuirui  corporis  incurrchtis ;  ergo  (Hniliter  alt» 
ti^Siom*.  Pr.  C.  attraSio  jequtvalet  impttlfiii  ^  ergOb 
1|t.'N.m«  ad  Pr«  N.A«  ad  hajosPf.  D.  A.  imflus  vi« 
rium  efideret  in  ttrrji  trahen^e ,  Jmul  tmitsii  ipjim  ttim 
hrttur  fntum  C«  A.  traberun^  a^m  ptpdp ,  qu$  ditn» 
fius  K.  A.  &C.  Corpus  rarum  miiiu^  trahitur'a  tern, 
quam  denfumi  fada  tamen  diiione  Corpora  aifllk)  de« 
tcrminantur  ad  eandem^eleritatcm ;  cum  enim  alBoiii 
iemper  itqualis  fit  reactfo  (  per  hgem  llt.  ^.  IV. )  , 
quo  minus  virlum  elidicur  i  corpare  raro,  boc  minO* 
revi  trahitur  corpiis  rarum,  quam  den(um.  Diatt 
tcmere  afieritur  corpus  rarum  minus  trafat  a  terra , 
quam  dcnrum ;  Cmt  cnim  attractiones  in  ratione  di« 
recta  maiTarum  attrabitinmm  <  §.  i6).  )  non  attraSa» 
rum  (  5«  166.  SthoL  IV.  legt  IV.  )*;*  crgd  cum  eadem 
9erra  traherc  ponatur  corpns  (ivc  denfum  ,  feu  rarum, 
ittrilimque  codeni  modo  trahcretur*  ]^.  D.  C.  h.  e. 
titrumque  ai  ewtdem  velocitatu  gradum  determinahmr 
C  Gt  ifo»  fhiret  molecula  attnSentur  in  corpore  deti^ 
(b  I  quam  raro  N*.  C.  Non  modo  ob  imminutam  di* 
fiantiam  fortius  trahuntur  corpora  ab  cadcm  terra,  fed 
etiam  ob  majorcm  mafTam  corporum  attraSorum; 
cum  cnim  &izid«  moleculc  tcrreftret  traham  fiiigQ* 

hs 


lii.4ili<iruin  «orporiifi  ^  >oc  f<Kdor  cflc  dcbct  mncdot 
pik(Qv^  corporis  dcnfi,  qu$im  rari^^ao  pluret  molecolati 
(ofitiact  iftudjKa  illo ,  nnfa  t»V  uiibafirti^.  Atquo 
uc  rem  iftam,  circa  quam  paralogifmi  freqaeai#t.Q60ttrt. 
rere  poflTaiu ,  &  (blenr,  cxpedttiiSm^m  habetmut,  duo 
e4ii^m^  itt¥fiii :  -I  mo  attraoiio9#|ii»ipccfiri,  qoctenoc 
fftd^rminfltio  Gorporis  %iii9iciu4uicmam  vihdta^ 

IC  illo4o  rumpta  refpicit  (blam.  mM^ti/si  tr.abefiten%|  &i 
44$hv)tias  ;   hinjc  c«c»  /.  &>  fchpL  dixi  f  Vthcitmt^afi^ 
VKo  «f^  ^f^^.  fmw»  trabimr  ,ab  alia  ^  ugwrm^fori^ 
hw.  V^^s  C'  maffa  €atpori$  aitrabnfu ,   «m^  auf^iBi^ 
I(i^^riorc  modo  tccepce  etiam   rc^kit  .ma^at    a^ 
irccrccj  cum  ciyip  fyjpU  pcrticiilc  |;fOTcftrea  unhiiM^ 
Jmtf^li^  corpofis  alt^rips  CQJuscupqi^  ,  tCtict  ic  rckpll 
O^rcrc  debctv4s  attrai^va  terrc,  qoot  (nm  MrticuS^ 
fO^pori/r  atcractl.    PiifDa  iUa  terioino  SchoHs  ufitacqii 
diciMlMh^^taccio  mst^tff,  fbrtior,  cttt  dcbilior :  poftrqei 
V^4x^ffytui  validior  ^  ci|t  rcmiffior*   '  Ulc  aBQ|ip||^li|||| 
cx  m^guiiuditti ,  ^  ^a^tati  JS^t^m  C  &  kc  dicemlii^ 
Cf|t }  ^  ifla  ex  f^i^lt  >  ^  ^requmtia.     In  caTn  |irsfGii-Y 
te  cxtenfivi  fortior  eft  f ttr4<iUo  paOiva  corporis  denlfj^ 
qoam  rari  :  non  inttnfivi  ;   proinde  pcr  reaflionem 
tt»Q»4tift  atcrajli  dcn(iOfjic#Uditi»i;  in  |crra  plas.ririnm 
oMteHji^  rumptcrami»  apn  immifivi.  ..    Indc  patet  ffc» 
6pqfif>  ju/  Qfufirm  I  ncmpc  D.A*  qnc^qirptti  impai*; 
Wt  eft^rcrifs  |  co  minus  reSftit  irnpul^i  squabiU  , 
icu  qiu  corpQrc  «mnic  «qualitcr  afiiclt  C. A«  iinpolfni  cc. 
pCPporttpnc  minori ,  q^^  proportionc  roinus  cft  corpuc 
iiipta^fttni  N.  A..i8c  C.  •  A4  P^b.  D.  A.  sqnivalct  im« 
jiifiii  maflic  impol^  prqporttouatq  C.  A,.  npn  pro- 
pOftiai^ata  N.  A.  &  <^f  f  tjficrt :  S^.^on  (empcr  impnU 
%C&mirs  ioipol^  prop^rtionata  ^  nec  crit  cttrafiio. 
%»jhl,4lp.  impmfip  cft  .quantitai ,  motas   nrforii  im.^ 
ffUimk^  proindc  #fltimandc  ex  cclcritatc  duAa  in  mtC 
iam  c)trsdein  imp^SinA\     Att^ftio  cuteia  non  cft  ipfii 
qoimitac  motoi  in  corporc  «ttrchcnte ,  ftd  cfficit  mo« 
.V       .  U  $  •        twn 


mpi^^ltt  l^  4nv48fioiiit  ti<it*Ǥ|ifiiir  ^i  raihm 
^mfSiei^i  9fi  tripiiM^  d^kmimrmm  mffa^  feUmer  «x^ 
pini  yfltwr;  nee  ^111100  qm  dfittm  «tcMAmicvit^ 
|§i|Wna  •(&  eaoAiNii  grtvicatciv  trgo^t  (itri*  - J|U 
«MMflctt  ctaAltiii  Mv  <^  p0iiu  kac  le^e»cxpof|i  pofi 
Am|  Qimiit  phMDintiiatgrtvttatif  corponnn  tsm  t^ 
w^Atimm^  qiiani  Mir^ijvOr  M«  yo/^  tirnftrium  N. 
1^1  %d!i  O*  m.  4S1  N.  C^  •  Dit»  atit  lcge  ttcrtaioiiif 

m^.\  tt  ipiiiifna  tmkfliunk  ,  'qux  iuxet  ;hfnc  (oltinF,  dl 
Wfinri^gtcn^pcriqi  d«beiit,ot  poub«aitxofltnfitin:  Coia 
OtBtiplHenoiraii  oorpa#uni  leindrA^itiovV^  ^ 
m/brium  "tmm  btetlogciCBngrotiir')  oudi^fliiMniOtf 
aOiicoripon»m  ocieftium,  'vm%t.  giaiiratit  ph«noflacQ| 
OtlMifiri  iMhiiiiI',  wc  cum  ti.u  Itgc  coogrotot ,  ^ 
fwhini  :  ^vitmnv  univer&Iein  corporum  td  htM 
4ittMiintct>  Ifg W|  r^rotfadfin  oflo,  ^  '    ' 

.]   VII.«,to  Me  Moofwi»  temit  nttiil  cicpltcotnf^ 
4Mm.c«*m  finiodioncm  iftnm^oflVcJuftm  gfflvittti% 
^ipiisdt  «ft^ttfQif  ^abrtrti  mfpma  grmA-jumf  ftim 
t/mil^  fnm    HtiiimfkiwaipKma^r  cmtffkm  tj^r Nm» 
tftm^  fuiimtr^  mth^'y^ffid^f9imtfiigttkff€rus  jm^ 
W  i^'  ^^Tif  i^witjirnf  \  mm^^imit  im  ^citin  .f^rmm 
Uf!h(i'^fm  fJi€ftommtitx''.^ttfiri7tmm  fimHL^  filffictrt  ai 
'  ^piimih  •mttia\^wmitt^>^em9tmittt^     &  mrs  atm 
kbmmmffmfits^ttiimlmtfin^pim  tttmmQimm  c&nm 
fmrfi:.imJitMgtiIm*fmm  fpnrtr  ^  mumakmmr^  mimdUam, 
pmit{mf,Mi^ammmfmmfl^iM  A  ^rp9M*im  smrfra  urtsm 
finiK-fidiHk^flifimmr  (i^wt^  fih^nifh^fim^ 
mump^  iku^mfit^^^M^  frk  •^madram  mSkr  ^^ 
Untl^i  ignoriitarttr  ^ittt  itlutn  000  fi>lmm  efff  eamtitth 
mmm^iimi^ii*Sf(mi^fmmi  V  o^i^i 
J^immmtliM  Mnfkmm  ^>\dmmttxmtf0imu^ 
.ilM«f!fi^o|tlr4#7itfiNfci| ,  <o«if /^  «Ai  imo^i  .  Atififwoi%  < 

Ifibtt^ili0^*f  <?iwiiiu*f  l^r  %mmmm  1  §\i  m  t%m^ . 


Hcc,  dc  Ms  fimilU  qui  ogg«rant,  rcnimndi  Umc 

W^iH»C  >sv<V'iM  »r«M(i',  q«w^«M4dMttSMi, 

-«HOk.jHliU  ^MwwigiM  iiPfMtoiai '  -        -  «r    M 

,    .     Obi«a!oiipt  •!!««.  ft  pmdaliA  pwitiiiiiil^  £» 


«    •      « 


j:* •   ♦'  «f 


C^ut  VII; 


De  tnm  w  imeiai  ceprm 

Met.  i  cgirv4  emnp  eli  .Ati«$,  liimiM-^w  /^*l 
(iiin'iiDfinic«b  pfnir^oiidiTer&tt  4iffi^«MM» 
'.AaiiMtVMB*'''      •'•    "■  ,•;;.....■■■;-,■'«»  I*» 

«ft  4eber^  qm  dinAlaMai  iiwWms>««plP»  ««Oyy 
U.  Corf)ti&  «m  Manun  »i ,  «.  e,  MMMr  iyyM|w*< 
Iwrfevenit  in  c^deni.i^Knftiwiit^tLiyjfeXlt  frtilid»  >V 
ilir«aionein  in  fii^lis  erbitc  puaaii  infle<Ut ,  vii 
«iie  «cccdae,  Mwilnftb!  11I.^<0mm»*W  nim 
«iptdsai  ntioni»  «flSt^iMMt  «na  flriwe)'««t-^  Vdbi» 
«UMicm  ntionia  fiM^m  iiw0Mte»  |«Mia(<^  »fF*' 
imdeitm.,.  (e<m»  flMiMU  MAna  liHMn  >4eftA«  (jfi 

KO;  qn*»  «ee  Md|M  »ii«t  «ylJiWwt^  «jgMf f *; 
nt.  Jl  am^irmn  HfOUwm  idtmiStmfiitf»^'*^ 
luc  «iniui  viret  ««dilmidege M«tom  MO«iem«,  »«ti 
MMrdMrofpoflonc.  <  IV.  ii^>fMftMiu»r  «(^•OfM«K»i 
nnn  W<livMifiiMdMif<^»  Mi«»Miy«rww  cl^' 
«ft^yttiMft  I  |iimiiii>rl«Mp<w  |Mf«fMn4««r)!««' 

V  S  *        (*'M* 


.d  I 


ftf  Mb JSL  Gtpmmi 


I 


loaibos  Pnfs  vi^rit  dooiir 
f.  «d  lioe  iiiiiB  m|«iri  «iti  «rrtrct 
dknaiom»  ^MPfcikiiit  -swr4l 
MO  hibeiirttr,  o4hiie  «iriy  tmukm  l^nm  fyjtuutes  ciir* 
fom  ddcribme.  Iftod^aQi  id  /•  97^^t>ottflf  opomtiry 
fid  cxddit  in9i|  lyiii^Httiiilfk  f41t  pM^"^  Scripto» 
•liis* 


M4  ^:  i^ff^^^i^mftdhtc^ 

•tmmm  liiimi  pcrpetoo  oigctor  (§•  if  )•  ) »  «litcr^ 
nn^mfiin^trix  imtqcj  qiiod  cmiom  celfrkM  «iDgea- 

rpro  rariene  imimiititc  diftantif  •  MKhl  d^  Roti^ 
iinet  ear^  dil&renli  djbetor  i4r  tmtri^tiii^  HL 
m  ^Nthtmd  pfiboit  |<  cnilhittr  ;  ^it  eorpn»  tr^t  av 
aiMHltiWffft  fiMI.  .  Vii  pi i/iflil»  eiiim  Ht  ibj^ 
ttl  loqfrMifeiSvtQdit,  qood  et  impoUiim  oiif  iHlbiill 
idttmr  fimmJkm  mgnium  mnut.  Qoibi^m  viret 
gftdhii'  |j|Minm|  m^gAmXgk  ^mA^^igdii  nonfloidMitiir. 

«rtl  iio  iiifipi  ■tjNtnmr  tii^  Um  corfi  eim  ftA» 
m—  iniit  iMMMi  pofieooi  ^  qood  timrt ,  nl  /tflV 
lit  «iMW  MoiM  mfinifftiittc»!' 

^^^^^      ^^^^^^^^^^^"^p^W      ^^^^^^^^^^^^^H     4i||B^^HM^^^^VV  '  ^W^^^^^^^^^ 

Bmiwrjotpi  t^mbhmioiii  ciwtm  ^tfei  dito» 
ift  A|ri:;  Uiic  01  fbMMi  eiltt  Jdiim  diCorroBt  e|f 
biiwJiM»  iioi^iv^llMiifte^  .^ 
tmpirfbiil  primmM.iltiioir)^       io  GAib»  ,  nim 
ylfim9(m9iAMfm  pm  w^tmm  eocmt.     E.  & 

$it  piiiiiti  iH  ioiM  ^  (  fq[«  )tf «  )  ,  qoi  primo  tifll» 
fttft^lo  vi  pnfiSM  ■mpiWiW  fioiilidom  dttemiiiit^ 
tioMm  \ixitm  4M.;  indiiintie  .Iftinpofeold  iti  i^Sii^* 
I9r  vi  tmm  Marii  fmfut  Mi»idtecgiHiifli»rttoi»  ol,  htc 
4k  fi  i>|tllfipniii|im  idtni«iitl^c«lwid«miw 
;       •  ;   «;  raet 


tttiqut  in  meaio  non  reQA»m  ^am  •»  prpiea«oo« 


rtidum  «ft ,  «M^  ffalMM  ^UcWfd  4MI9W  JF>i 
0,  Olt  &e.  Di^eaaUi  Utm  MoHMKoha  iitfwM 
Crvif  dc6ri|ittf  Itidem  Infinltc  p«rm  <<^  «f*^  i 
bcbitnr  ittqo*  lerict' n^taif«i«  «tairuiitinihito  p«« 

mom.  «e  divcHtoi  diN€tioii«ii  MnntM ;  ftMi 


'Wlit' 


itt  eondpl  ftlil  |«Mfii  «wwe  |MMi««  *•• 
pfcB, :  fWw  •*#  i-^jta»  «1«  «•«»*««••*. 
4fai*(i,  Mr«Mte«^.»i2l  fBe4«nHkmidelMK«iK 
M^ad  fmnltf  bmi  aiMm»    lik#«mNr6  nonn*. 

Inm  «ft  ex  i^  Ai  O*; /«r  ?A»  «Mtf/W.»»«»  ^rr^ 
Hk  tioo  intelllgi  rim,  ^«c  cqicBbo*  t«»fotth<t»^ 

?M*Kt  l{)afia  dkcofwt ;  petet  enim  llB«f  AM ,  *£* 
l^.  4f  .1  ieqmlci  m«  ^  y  im*»  Jf^f***^ 
MftnKi  MH4m>«l  «nmrteMi  tii«qni»i  <P*»*?*""* 

Dam  <rm»  •#  •rJiJipfr  Ws  ttnifiiMdi  dtdjtBr ;  nb^ 
4ieimrNlMe«d«tofr«WMftir,  ^  fimfcr«ft««<«^ 


A 


ti#       0m>m 


kHMfi%^9  9flm  |Ni(farMia  aontaxac  dmi 
Mfiiur  tahqdaiti  €  ^daabas  illis  refiikans  ; 
^onnfticque  iti'  eo ;  aaod  nvobile  percurrens 
i|i:cu(i^^mn|il  tg/ffih€UC€  determinet^r.  ad.r^^ 
oifiiMP'.  w  .4fcp  ^  ^up  pcr  Xui^tsk  f  lorfiis 
iKei^^<qMf  vmKirar  yim  oemrtpraioi» 
diffiftiDHt  cDmraria,  In.fisperiore  4igu-^ 
NT  vj/  OmifiBHi  indfc^fti^  per  lineas  if  D/fl^i 
ttf  9t^.    'TsHffMtliAs  per  tangentes  ^i^  £G| 

fe /?niq  f^j]s  ,gpjiqtua\ib^^  rfcc^ret 

m  centro  fm  motas  > ,  iHpyi|»aiyiBtcgvyiai|»% 
conque  elaberenir« 

sreom  firmil  fie#  «mi  tenitilbgtoi  ler  tan« 
gfentiaK  naram '  'fypMitici  detdrmfnetiir  zi 
rccelTum  ab*  artuf  efl  '«hfm  vls  centrifuga; 
jerprmii^iQ^  quiatn;habef^t  Qprpus^^apeun"* 
dir  pooiis  a4  puOj^in.  jcp^pmum  t^^i^ntis 
Ibk^  inortti  omiMktgdm^A mSs  iwi  smiri» 

nlbirt  «-eu^si^qaod  reYew^bit  db  irMr«en«: 

^peum  id^itafri  n  inertfie^    '"    '   •*  *     V 

1 

Oftt.  yif  ergo  ceutrffi^g  eorperif  fimpermiMr 
^,!i^i€agffftji€l(  2  cafoi,  veloti  eflSs^os  coQudepri  &• 
wi;  (emperenini  lif 'treji^'%r^  cbndpln^  fefinite 
prv«it ,  Infinfties  'nM^o¥«  iMF¥lhg(ni ,  qtiani  cRttuiAa^ 
tii>sentii  ab  eron  <|hi^  JMififliM^: .  SU«iMI^ 
Ml|f<iconiia  ooiimiUl  ^qrt.>il  >  il  im|f fcfli  m  taa*/ 


^9sftoiidU^  incthH  Mcttm  iflirtttii  iKiSp9id&i  aoc  l^ 
^ificaADftil  ignoriitfd  ifiiiHin ,  qaantof  errofet  ih^« 
jcic!  Ffoc  it«que  diftHlnen  eifo  f  ifho  Vis<eentnfaA 
ikmftt  'eft  =)  ctnttifttt  f  nott  item  t«igeAtiim 
sdo  :  |)rojedionis  meilfiM  ^ft  tivfihities  mefoi',  qiM^r 
fiienrura  ris  centriftigflr.  jtto  %  Vlt  ttfhgentitifl»  Wk 
^ftcundtiin  dlredioncni  •rctii^-eentrifiigt  &ctindiiih< 
'pdrtes  centro  virium  oppdfittf  •  4tb  t  TtngentitHb 
cttmcentri^pett  vi  con^rant  vere  mdttiin  eflficit ,  ncH 
centtlfoga  ;  hccf  elnm  ^ireAe  cuHi  opfHmttnr  vi  CM* 
itilMt»,'altert  tltertitr  etfd^  ;  neqtM-^oMM  feremr 
^n  curvt ,  (ed  dantatit  fecundum  dire£Uonem  sn  for« 
'iftdi^is.  Qaid  ?  quod  vli  cebtrifaga  tft  Vis  fnerf  ptf/^vtf» 
ift  tontraria  ce|itripet«;  ttngeniitlit  iifif/tw , '  ni^cj^ 
ccntripets  eonrrtrit#*  ^^Mtr  miir«n>, 'Alttif  No^ 
llle  tik  vi  centripett ,  ;flt  c^nttlfiiga  ^^fiimm  ptjfn^i 
/Ua  enifn  efi  vis  oBhmi  qiitf  ftatnm  tt)dftmiimin  otte.^ 
&  ad  cenl^nim  dirigir,  kn^^fmH' f^fhH'  Hat  miuim 
rutn  conditionati  requinfreceffitmyUf  wreui^  emf^Hkm 
pro  cafuy  in  quo  iUa  non  a^t :  non  atfolnti  ;  uU  mt^ 
/  tem  /Ot  WyS  ,  fltmri  &g^m  fittitm'  \  Himifum  i^ 
fcenfnm  cptporit  a  iangfuH^  sd  arftk^t*"  ^     -  ^  tv  .  .^  ^ 

Sdol.  Objlcimr  t  Mdfoa  earvU&Miit  remi  H*» 

IJbitar  e>c  vi  cenrripett;  0c  ocmrilnga;  dimr  ei|;e^  vto 

"l^ntirifngi ,  neeitt  i^id  ineile  imtgi^ffom/    Pf.  A* 

'  tmn  vh  Centripeti  majorl  dll  ^  "^aam  eentiifagi  ,  IM* 

bile  WceiUt  M  ctntmm  f  tnm  mitm  i  IreceAkl;  <rg6« 

)|t.  N.  A.^  Vfret  hc  fimt  oppolrgr,  fllroinde  fneompi- 

nibilet ,  nciqae  fimol  imqiiim^ntHlitirt ,  iw  *eti(hM 

fottxknt:  AdPr.  R*A*  icctflbi,  vel  fcMflillilli  pMri^ 

def  ib  ifltnlti  qtiem  femiit  difeOie  M|iiilii^oiit 

ireAt  id  eenfrum  doiti.    Ae  Meei  U  Hegirhlfilll^M^ 

ieft  iii  inotti  et^iliHid  idefll  vinf  eentvtftigitti  |  'mk 

cntm  Arviiineat  maMtriminii tMipl^f I  mndetHt 

sion  t«  vt  etAtri|^i  ^ '  <k  eenlrifagir      '1^»-  W  cifmi^ 


i 


irab ,  ^nm  qaod  mobik  iiolr4t(cfpdim  t 
•d  •rcim ,  fir  non  «clcflet.  vii  mnripeca  «d  dticettfiM 
4»Utmimn$ ;  binc  id  |  qaod  tttm  iK>n  ficrct ,  cocici^ 
jpittttt  tcnqttisi  &OWI  ia  f&mm  comrariftin,  flt  com* 
Mntitii  cjiMI  ^ffcQiii  ctuflcm  focndcin  fingimiit,  qtic« 
^fim  ccntrifagcm  cppcUaoim»  -  Ditts  IL  lEm  thdg^ 
0i§  dcmonftrinc  Phjritci :  o6rpiis  osmc  in  gyroc  cAmn 
«cacipcrc  vlm  ccnnrifngcm.  jB.  b.  e  niri  mic  por  9^ 
jcatcm  cUcorc  vi  ccnrrinctc  C*  tiW|uaro  6  vic  ocacri» 
•Sigc  c  «oigcacicli  difiinttc  moi«m  qtmdcnk  cffidci  K« 

II.  Vii  ^oirifimc  hcbct  diqncm  cCcfincc  ;  qfUL 
Wk  dctnr  }  Pr.  A.  cffcftiii  vjui  ccntrifojrc  cft  dctcrni* 
gatie  ccfiiircndi  miyorem  c  ccniro  diftioticm ,  fi  rtt 
•idic  aoa  i«^>tdicr.  ^.  babct  cliiiocm  cffcdom  im> 
;^c  €9ktipifu^  moJ»  C  A.  rtslitir  K.  A.  &  C     Ad 

iactio  iUc  tft  ipic  vit  ccmctfiim  aw 


UL  Vic#cntiifii|ccicvidciiipcaiv»fi%fogpMOC 
ri  ccntripcM»  flc  cudcnc  pcrtcm  cHfBcm  gffirSctic; 
JcfgOt  Fr.  A.  Vii  ccmriiffigc  cx  motn  dmrim  tc^* 
Jlfm  mm  coiamaiiitcr  diciciir  dttrdtcrc  ciiqaid  dc  gro» 
fimii^  forporum  »  ploi  qaidcm  fiib  jBqacrorc,  micpc 
od  paloc  i  andc  cticm  Phyiiei  ca  (uUcic  aipriikrtt^ 
,  icpciaat  %uccm  tcrco,  c4  poloi  coflipfaflcm  >  •  U4^ 
Cam  i^imr  4e  griivitciii  mcnlbrc »  boic  pcr  obftrfc* 
ticiicc  mvcata  c^di  iblct  menrura  vic  ccmrifiigri  ^o* 

rctar  cliderc  pcricm  grcvitctii  ;   crgo  cft  vii  cfttcc 
N.  A.  c4  Pr.  I.  D.  A«  vii  cfmriftfigc  cx  moto  dir 
<  arpa  «cciia  deircbit  diquid  de  grcdtctc  corporoct  ^   4 
mrmmr  C  A-.t-cc/lifrN.A,  %iC    AdPr.  11«  0.  A.' 
icac  iwwitciic  anafiiro  cddttar  mctiforc  vfc  ccntriliM 
go»  idE|i|c  idcos  ^nift  pcopCMi  mcrum  eoaummcoi^ 

Ccincitic  corporc  cam  ccrfc  moventur,  pcrt  cfe* 
Mcaimiic  nnriic  noirii  fahihfimrr  A    fil  idcCk 


V 


1 


A  Mmi  idmM  9t| 

filt  i<l>m  MvlNKii  iUbkM  *t  Ti^etrtriftiit  dk 
miinif  K»4»«G«  I»dt«  toiiilNM^v  qQtf|^ 
Ibcndit )  fnoftttir  ttrrt  aioto  molutioiiit  icirct  txcoi 
Ifaniii ,  tniwtitt  tt  iiti»eiui  ttftroliftmtt^,  qntisi  oot* 
piii^  i^^iblttiitiir  ;»fim  Ttro^oNmtibr^Mii  tAM» 
Ctt  fiMn  i  Ite  lit#Qt  corporii  iktrioi  inttum  cM^^mn^ 
M  €M^tmiim^  I nde  eft  ;  daod  IbliM  tr^f  f^t fc  tlll* 
Ihmi  i9mfM^0hmm  fnitiri  fotitims  ^  lobdoQt  6c<illt 
I^Hiitttriim  ptrtt  tflfidiit  tf/UM  ,  ^  ptri  ftmpifr 
pftitift  tiRtt  eft ,  qotitttai  detrdhatc  rk  wiAtiM^ 
fi  virttgtiet',  noUiqttt  ^tiKttit  coni  rr  tentrifc|t 

«iitret.  Seiii  JSgtrt  tg*  4k  trtftMt  ANAttscM  ni«# 
[)o  :  5ff  oifervm^P  §h  fipir/Me  terw  t^nfiimm » 
'ifii  iu  B  4mim9  grsm  ,  fttif  /lU'  nltOmm  pi$dmm 
"Hmpiffiuh  devenim  ml  puifim^  E  rfSm  BA  im^r^ 
m^im  dimm  trmiskue  im  hts.  FhMimr  iffi  frrfi*^ 
tifft  mdend^  j^rM»  BE ,  f9  mmmid  rt  ikrm  fet^ 
"^it'  Jpmmm  tMu^  tmijm  j  -  mmmtmi  Te^mrit  mef^imm 
^  mmrifvgm.  Nm  rtOu  B  B  A  mtm  dhirim  trmth 
ImMin  Iftu  per  itrmmBt^  4f  m  timu/mH  BD  i^lto 
ftr  fi^mimn  i  IX  mettjkrmtt  9*  tmmffigm. '  Fi  imrtki 
^tiMfii  gr4ve  iUud  per  BD  ht  D.  109m  imtegir 
"grmfituUt  e/lDhey  frm  jfm  $ijl$$m^  film^  i  e  A* 
^Tewettiut  mmmtefm  ^  tm  ^w  cein^^nt  tgttttr  tttmi  m^ 
trtdnt  de  grtvitmlt  ^^fkOm  1»  f rttNMii  4^/Ziiijfil  »«IMp 
hthtttr  integer  Iflr  ^eSm  X>le  i  tiet  pr^ide  mm 
grmnmt  mfm »  ^  %fit$f  mr»  tBdttj  fid  tnfirm  tf^ 
Jirvtuittd  fiiUmntttr  pnrs  dfi^  ktdmu  mt^fimim  #» 
^^km  tmt^s  nk  eenir^fiMi  l^tBm  re^fitSivm 
ttfpeSu  m^fljti  tf?  MJtir  i^Su  ttfiimt ;  iffitti  tMliiii 

nPMfMiVr  I  liPif  mmUm*      /zTnv  ivvii  wenmmeur  uu  tutegntt^ 
ipr  w  ttuwyUgm-^  jtm  vcuut  wt^trm  m  miftev  mevtm  ttt 

'  futtt  jtmmitttiir  ^  omimmpi  HMMitttii^  1  ^  tNt  ttutwi» 
fim^  •BitM  tgh  t  V  miir  rtnwii»  m»  m\\\'it  ife 
jP^tm^  j^tjjtvtmmtF  tgttm  ^ttttfmmmh    Tif^oe  Mie  i^t  mi 

ttoflt ,  «od  iMbii  iMtr  tpptreM  injKfir  tfMot  gfi* 
fktltt  »  Itd  MiMIMltM^  ficiUt  fiM  cni^tiffiM  ctn# 


^  1 


'. 


•  -u 


j^      JHM»  fii'  fi^€oqp«t  alioQod  •  fclcro  Aflmtstor  | 
^      jMnBOprcfiMt  <  fll  iflft,  *«  fUcr»  vi  gravitMis  &•» 

^nim  ibaificaiu  ,-4»?  oorpnt  Mcno  iiiiiixom  J«iflmt 
«DOttovoH»  ttide  fcro  tltiidi  fi  tioa.  o  vi .ooairifiipf 
.Ditor  ^go^  tHk  i^  M*  N.  m*  Indk  iioc  mnoM 
^BB c^ ^  ^odfflnviioo  toftt fokri»  qoom  noipirio  A^ 
Anoid  forccti  ^omiiwt  eifeaui  fi)rtiociir ,  non  pk» 
^pom  offci^ma. .;  N^jpi  fi  otroinqiio  liler^  coderet^  niil» 
Ipm.prcfiionom^fiillirccAdcnim,  oiiio  (e  pcoffipiii  cor* 
i.9oriiitPorprtM.  r«ib#oQirol ,  .&  .otnoifoo  ,  gioviecs  pk» 
.iwm  ofif  dom  &iitret|Hr  >  ergo  Ui  ^om  m^  qoo  ^ 
girove'  &  fiiknim  ^iiovmmr  01191  terro  mota  commii^ 
'31 ,  4(^  cnm^co  .comimm.deibeBdont  fper  ipetiom  O  h 

igremooem  fiyiiic»'^  «^.griVilBt  ^poric  fiiftentaii  olU 
«flftim  (olomaiodo^pcirtem  elfedui  foFtietor.    Sdlic^i: 
lieft  COHCipi  graWlct  .reiQ|iH«  in  doei  pariet»  cfltoorttKi 
t^o.  deice^uim  fOMrct  ffr»i>  h »  pknom  cnoftomt 
i^A  %  oktci|atoieiliiit4ito^eflioiiem  tii  fotani^i 


-jfiel 


*'  *^^f;i7r/  w/cr4mwifa*i|)Tifii»*<«  f» 
*^e  drca  ax<;ffr  fbum  ^  fiir#  drc;i  pQnftiitf](cli* 
j^qdod  extra  J(f  pofitom  reyb)ValhtUf )  nUunm 
^m  tnaro  abiir$  firtaHgtnttm^  cijffdntt  %A  fntripdSk 
«.Mpcui  emm  jgynin^iiis  na^hur  a  vi  capgini^ 
"liaU  aecenrrumiaf  ergo  bac  tfeflTante  obride^ 
^liitiHeelfiiAiitiiiiittifi,  ft  mobile  abiUt  p«f 
>lafigtHtfem#  ^Obvii  txpteflVnehta  hfOttti  httili 

iHltoiltiftuiii  fteiitnt  s  '■  im.  Mit  eoriroiitii  ei» 


1 


f 


t 

\ 


l^ter  MtoItttiB  aquiin »  aot  Itttttm  latiffima 
diCpttgunu  3do»  Sf  nammus  tabula:  fitum 
honKonti  parallcium  habenti  imponatur»  H 
tabula  m  gyrum  agatur^  jam  nummKS  gyra^ 
bit  €um  tabula  »  jain  dccfdet ;  gyrabit  cum 
tabula  I  quamdiu  motus  tardiulcuius  cft  % 
decidcr»  fi  Telociot }  gyrabit»  quia  propter 
fiiabras  fliperficies  tabuur »  &  nummi »  paulo  >' 
firmtus  tabulsp  adhxret  nfimmus  »  quae  iD(« 
quaiis  qualts  adhrfio  confiderari  poteftinftaf 
vis  cemralis  nummo  in  tabola  retmenda  ru& 
ficientis^  quamdiu  motuseft  tatdus*  DecU 
det  I  fi  motus  tabulc  fit  telocior  i  quia  ob 
HtiAam  vim  tangentialem  JFacile  fiiperatuf 
tnodica  illa  adhaefio  |  quas  vtce  futigitur  tris 
eentralis  $  hac  eiifa  nummum  decidere  ed 
fieceffei  ^tio  :  Lapis  )n  funda  circomaftui 
peripheriam  clrcuti  defiuribtti  funemque  ten* 
dit,  Nempe  t  conctpi  pofeH  lapidem  Hlum 
T  egitati  geminis  viribust  altera  ^^jcSl/f  &  /?« 
Hstd  y  quam  manttf  ipfi  imptimtt  i  altera  i^ 
niii  foPifs  9/L  p^p9i»o^  ^^^1  neit)pe  refiften^ 
tia  funis  I  quer  conctpt  debet  tanquam  cauffil 
laptdem  nrgc^s  verfus  manum  |  aut  fiiltem  tti 
circumfefentia  retinens  \^  fac  enim  i  funls 
tion  adfit  I  con^nuo  lapis  recedet  a  mantt  | 
tutn  gf avitaie  fua  i  tum »  Ac  vel  maxtme  i  vi 
firojedlotiis  iaspolfus  i  fed  recefltim  buno 
«ohtbet  refifiende  hmk  Intetea  Vtro.teiH 
dttur  funts  I  cur  1  niii  qiiU  nititur  tapis  re» 
eedefe  i  manu  QiB^nfidttm^  diredlenem  tan« 
gfntis  i  It  tiM  am^lftts  tenditttri  quo  validiof 

X  fft 

■  / 

J 


«d  motus  lapidi  imprefliis^  itini  h0e<amp)iiif ! 
lutitur  lapis  recedere  a  centro'&it  mpuis.g 
qi|fi , tehemenr tor  fueric  motus  ^rojei^liiis  | 
prbtncie'&  amplias,  fums    diOendt  deber^- 
Sttbinde  autem  rupro  fune  Upil.celerrimo' 
niotu«  abit  (ecundom  tangeqtem  ;  rHbJata  e* 
fsim  reftOemia  funis  (  quae  eft  eat»fra  tmpe^ 
diens  i  quo  minos  lapis  moru  proje^li  tais#4 
getftem  £t)guiia  momencis  incboatam  pro(e« 
ouaiur),  fola  ?is  profeiftflis  efFe^m  forctri 
oebet  iMundam  diredionem  (iiam.  r 

Sci$L  Cotiatom  zhennil  (ectindem  nmgtnleirif' 
floniiulli  focaiir  vim  ctntrifiigMm ,  qao  fiomineii  aliud^ 
nihU  tnt^lltguiif ,  faicbor  cuni  iUis  i  corj^efs  gyrsiicia 
eencipisre  vlm  centrifugam .;  qol  loqoendi  mod^s  ell^ 
^oidem  frequentiori  inihi  tsmen  minos  ad  rfgorfin 
exadus  videtur  proptefea  .*  quod  vls  ccntrifuga  ^  ot 
dixt  I  (it  merc  pafliva ,  (blumque  ex  vi  tangcnriali ,  & 
iherti»  refoieer.  Deinct^s  tamcn  fcrviam  frequeticidri 
d(  confactodini* 

4*  17^1  :h  icf!f$tAui  u^OHtibm  i^t-m^ 
dj^  jU  Mila  t4i€mififug4  ^  quo  majm"  tfi  ^htHsff 
IjT  maffa  carp^rif  in  cir€umfirintia  matu  VtU 
Slium  itaque  a  Vilockatt  corporis  gyramk  repe* 
tsKidam  ede  quantitaeem  ¥is  illius  cemrtfti^ 
gs  p  patet  ex  di<dis  §.  praecedenti ;  tnaiovi 
Aniifv  velocitatt  corporis  gyralitis  reiponde^ 
re  debet  major  ¥ts  pii^ofediiis  y  ^  qt^^  na(ci« 
for  mator  tis  cemrtfuga.  Ettamque  a  maf^ 
aarporii  gyrantis  penderio^  quamitaitem  vis 
ceatrifogss   aoaKta  «t   ttporitaenii»  Cl^ 

JHciUt^ 

\ 
\ 

L         ■     . 


ikla^    Si  globus  Vtmus  vp^^  Ga&  kiftra*^ 

Aus  i  6t  A^ua  repletas  (  cui  tamen  tliqmd 
celaf^H  olet  terebintbinr  6t  peitnixtum  )|- 
ope  tnanubrii  velociter  circumagarur  /  divi« 
detur  primo  bleum  in  minutiliimos  giobulos 
iquac  innatantes  >  qui  renfifn  motu  rorationii 
#1;^ epti  non  i^l  centrucn  £;lf  bl  |  fed  in  cy lin» 
drum  quendatpv  axi  paraMflum  colligentur^ 
lo  eundem  cyliiKirum  diibit»a^i fi  proolea 
torebinthino  fenBbtUs  «jutdem  portto  ilHtii 
femineat*    Nimirum  tquf  denfior  eft  oIeO|^ 
^el  s^re }  magtsitaque  recedit  a  centro  rAo* 

•     4  .»»  ...  ■«.' 


qUAm  delatus  eft  ( ii  aidl  td  hotltotkti  paralklut  ^ 
llf  m  inclinaco  i)(8i  abit  ad  (iiperipfeni  polmn  ^  <  .  %« 
fuia  globulp  iiji<iQifittim  ab.a^  iiRmi  non  tam  ci^cf 
^minutiicari  fgtfsSL  ce leritai »  qoaai  a^tix  i  \itxc  (^tiil 
I^QaHi  #11  yi^^ii  i  maflain  fuppletua  etlaritatc^ 

CQrdO^  h  .  Menfdra  proUi4e  vis  eentrifagi;  ti 
M  C>  five  itiaita  duaa  in  ceieritateitt*  Vel  ideo  i  fi 
M:^  m  i  eruot  earutidem  tires  ctntrifugar  iti  ratlonf 
direfta  <;€lerttatuni  j  fli  ii  C  a  1 1  erimtin  rjktioni  «U« 
ffafia  ffliflarttiti* 

Cyfatf«  II,  Si  T  Sl  (i  aft C: «  S  <?<;  ( |«  01« 

Scbql  IV. ) «    fpatii  decurla  a  eorporibas  gjrrantibua 

funt  peripheritt  Vel  aTCQi  ^  argo  celf ritates  «qrpeniqi 
gyrantium  runc  ut  pcripiicrrdt  ^  i^l  arcusi  '  CTcrrpofa 
^^  lor^ul  a^  ^^iiatora  diftanu^boe  ininorcm  pe^. 


1 

i 


fS4  SfShti.  OifmVIh 


fhcriifii  CMimvini  cmn  tcm  moni  ratigititi  tb(bk 
vimt  <tft'«ntm  figQrt  tvrrx  td  poloi  cofnffirtfli ,  t4* 
4flCqiitfortm  procnbtrtnt )  ;  trgo  mtjori  ctktictM  fe* 
ffnncor  td^ottortm »  qotm  tci  polot-^  oniocirct  vim. 
omirifugtm  mtjortm  e0t  opor(tt  ad.  JEqatt'»rccn  ^ 
^am  td  pplo$«    Qoid  vera  vis  centrifuga  conitdcrari 

Ectll  QC  contraria  gravitati ,  &  veloti  de  ea  aliqoid' 
trabcnt »  hine  grtvtort  (bnt  corport  td  poloa,  qottir 
td  ASqiitiorem.      Rtm  gtomerrict ,  ied  dilucide  fie 

fm  mrm  ^  A  B  dkmmr  AEqnMm  urftfirli  Is^tm 
\  frt  t9mfi9 .  ffusrum  Hrr^  C^  ac  D  E  ftmt  •*  diameter, 
farjdltli  tujnivif  artuli  ^  cujm  cenmm  erit  iu  E  in 
MX9  Pfffo  remotim  «  Cf»irt  amtCf  quo  hcm  0 
/kiris  rtmmior  ak  JEfimtort  A^  Ef  ^tffit  foh  P. 

Xuprtmk  ^  qutnitm  j»  ftovk  cirtulari  mm  vff 

ttntr^sa  dirigitut^  ad  ftrttt  opfoftm  etutrt  timdt 

dt/iriptt  ^   iu  A  dMgttur  ad  fortet  cfpofitm  ttntrt 

Tkrra  C  ptr  AC^  in  D  ad  ptrtts  oppofitat  ctfitft  c/r. 

cn/i  E  ptr  E  D*     Gravitat  antem  uliqut  dirigitnr  p 

falttnt  ad  Jeufum  i  4d  tetttrnm  terrd  C ,  nimirum  tn 

A  ptr  AC^  inD  ptr  t>C.     Otm  igi^r  AreSio  C  A 

fit  ftnitm  ttntraria  dirtBionl  A  C\ff  dirtBio  E  O 

40  minm   opponatur  dtrtBioni  D  C^  fuo'  puntiitm  D 

wtag/lt  rtctdit  ab  Mqnntore  A,  ^  ne^dit  nd  poium  F  t 

fait$  Jbh  J^ttatort  vim  Centrifitgmn  tjjt  pmitrts  cot^ 

"  trnriam  vi  graviiaiit ,  in  ali»  autem  locit  minm  4& 

ttlte  ipfi  oppoui ;  t^  eo  minut ,  tpto  majii  reetditur  ai 

M^ntort ,  E^  acctditur  ad  polum$ 

ht*^rfa  ubi  phres.cireuH  todtm  emptrt  defiri^ 
hmeur » virei  een^ripeta  fuat  (  vide^.  |S4.  Corotii  V.^ 
fn  eirenlttfim  radii  ^  quibm  vfrihn  viret  eentrifitgm  ^ 
qnantt^  (^  t7o.J*  Quare  vie  cemrffitga  in  u  tfie 
^  vim  eitnWngam  in  A^  ttt  D  EadAC^  fitn  prt^ 
ttimt  adlbCi  mnfi  ut  fintf^  D  f  fnimirmitfiinifdl» 

y  !^ 

( 

fl 


^m^^  Ud  0  f$lo  )  04  r^hm,  Ba  mtttm  nm»  9$ 
tifimr  tfi  ,  jif»  low  D  p»pgu  rtadit  ab  jEfMon  ^ 
if  ffiagir' dccidit  ad  paium  P^  n  wog/idecrefiinm 
D  E^  Igitur  ipfi  v4f  witrifitga  fii^  JEquatOf^  fitidnt^ 
tfimtkttima  ,  tum  in  accejfu  ad  fohm  t»  minor^  fm 
magifad  ipfum  polum  acctditur* 

Eu  igitur  di/9  capita  ,  tx  quiiult  vir  antrifnga  m 
mruta  dnrabit  dt  grapitUtf  ,  quo  tttagir  ad  potum  acea^ 
ditur,  '  J^uif  uimirum  quo  magit  acHtiitur  ad  polum^ 
ep  magie  decntfiit  ipfa  vis  etntrifuga^  ^M  iii  ipfo  poiu 
tvatiit  nuUa  ;  if  quia  ea  miuut  tUreSe  oppattitur  gravit 
ratit  direSioni  iffim  direHio^ 

§.  173.  J^wuttttfua  Up  mtHanHnt^  mn  ra» 

tmrJetur  mattu^  is  Hmfttfcuk  itfjfttili  pmrvaffa  0^ 
qnabili  habtri  patt/l  i  nam  (pitiam  umpt^idb  itpm 
jmitt  pmrva  decuriufn  irideitt  iqfihue  parvum 
eft,  quod  fi  in  (ef  tantnm  ipefteruri  i^ulla  tit 
eoconcipi  poteft  velocitatis  ina^gualitas,  nttl« 
Ittsqae  ileicus ,.  quantumvis  fi  cum  /e<]aentt«r 
bus  comparetur»  poifif  fi»a  celertutis  »  fttt 
&re<9:Yonis  mutatto  aliqua  concipt.  Bx  tu^' 
dtm  injlniu  patrvitatis  ra/^atte  anitattn^  nMtt] 
Ht^nitt/liSat  pra  rtSa  Ukari  poH^^ 

V 

$ri74t  ^ujMtttfua  Jti0  uettUrttutt^uut  r0 
tardttnr  tnatus^  fttnper  is  umpufenh  aumt  mM^ 
mo'^  fid  adiue  fitttto »  pro  tu$m  utufmttiter  inte^ 
krana^  ant  ratarjstn  tmltari  pattrit.  Dtmi  Im 
mota  uniformtter  accelerato  fpatia  {tmt  n^ 
quadrata  temporum  <§.  l6a)  1  aequt  etiartv 
ipatia^  ijnnennqwt  vf  etm^ttu  verfus  centfum 

aeicriptr  fiint  ut  qaadrata  in£Uotl«m  1  iiv 


qam  breviflhnuiii  illad  remptis  dhridt  pifleft  ; 
trgo,    Pr,  ni,  StntP,  ^'/i,  rriapunAa  arciis 
minimi  currap  ^cujiisvis  APD  (fig.  3?,)  pote* 
tnnt  arcus  illiinfinir^parvip^.jg^^  in  quos 
^iviflis  fuit  arcus  P  J^p^  haUefi  pto  ufiifn-nrit^, 
defcriptis  (  jf,  pratc, ) ;  erga  fpatia-  P  ^Pp 
tknt  ot  parres  parvr  illius  ceniporis  1  ,  quo 
de(bripcos  foit  arcns  P  j^p ,  computando  ab 
Mftanrty  qno  corpus  orat  tn  P,     Agatur  jaot 
f  K  cangens  arcus  P  Q^ ;  exhibebit  ea  di«* 
rd(^ionem|  quicorpus  fota  vi.prbje^ili  ani* 
inacmn  movcrerur*    E  virium  centro  S  du- 
Cioeur  radii  yt&v^%  SP^  SR^  SF  ufque  ad 
Ungf ntem  prodii^i ;  inde  patebic  1  mo :  U» 
neis  J^Rfp^  ^  defignari  effe^us  vis  centnpo* 
t9  »  bis  enim  iinealU  corpus  fola  vi  tan^ren* 
fiali  impulfum  re^deret  a  cemromocus  futr 
adoi  Radios  vea:ores  SP^  SJ^^  S  F  polfoi 
abfque  ullo  erraocii  periculo  haDeri  pro  pa* 
ralieiis^  ponumur  enim  infinice  propuiqtu, 
Denique  per  tUafria  ptin<^a  P>^i  fi  defcri« 
l^;|tHr  cir^uius  PBN.i  arctis  P  J^p  eric  eriam 
arcus  curVas  4  ?Z),  hinc  circulus  ille  curvata: 
olculari  dicicurt    Ex  pun£i:o  P  ducacar  dia« 
■Mieer  P  JV»  quc  perpendicularts  erit  ad  ran« 
gifiiem  P  K8i  circuio,,  Sr  curvat  communemi 
(p^Qfom.)\  fimiLl  ex  pundis  2j  P  ^"can* 
tur42/i  pi  perpendicutares  ad  eandem  PK% 
ittm  OJB^  p  H  "perpendiculares  ad  diame* 
trwwFM    Peflreinoagancur^2/,/>W. 

Hk  J«  canftitoris  fic  arguo  %  Ala  PPif^ 

ffif  (bat^reftangula  ( inufhmt  Wm  dt4« 

iiwtra  - 


mmo  aipcnli,  &  Iineol«:P^,>/ttin?(cqC 

fiiliiiter  tt&^  ,  utpbtQ  r*  Ay^biA.  infin^tc  piib 

v«  )  •    Quod  fi  e  (tnguloruni  £fc)#rum  angti^ 

)is  re<5bis   demittatur  pcrpendfcularis  i  erif 

EP^<^   P^N.ScH  Pp  <^  PpNipeP 

Cfom.)\  c^ujrefi/'!  P^tr:  P^g^t  PiV?    » 

P  2}  ^  ^^^  f^i  H«m  HP:  ?;rz:  Ppi 

i>N,  UP  pt  -s  HP  ^  P  N.      Qiiia  vera 

«(jualia  ad  atqualia  eandem  di^unr  rationem^ 

habetur  P^  i  P pt  =3  £"/>  yiPN:  i/PSt* 

>/s^,  2S  £/*:  «P  (terrtiiro$rcilicet  ratfenh^ 

fecunds  per  eandenj  quadtitaiem  PN  liM* 

dendo);  «c  quia  EP  :=  JQJ^  inmHpTtp^ 

fict  f>  ^  :  P,p%  =:  ^/:  ^  1.      Sed  etianf 

AJa  RJ^I^  ^  fPl  fum  rimilia ;  nlni  prdi 

pter  parattelas^/  9  Sc  pt^  anguhA  exfernt^ 

jrquarar  interno  ad  eandem  partem  bppon^ 

tb>  iiinc  F<^=;:  /t/^j  ex  eadetn  ration^' 

angului  /  R,^^  angolo  iJFp,  cum  fimilU^ 

ter  p  F  9  tc  R  ^  fint.  parallelat  ;     quocirct 

JU  t  pi  rs   J^Rt  pFa  Pj^  :  Ppi  {  ptr 

ae.  ///,  §•  L  ) ;  ergo  cum  \mtx  QJR^  ic  p  F 

defignem  efTedits  vi$  centratHi  P  ^attterA,- 

6c  P  p  tempora  ,  paret  :   xn  cujusvis  curva^ 

arcu  minimo  effeAus  vis  centralts   efie  UC 

quadrara  tenlporum^    pr^nde* 

CoroU»  'Semper  lo  motQ  aniformlter  ai!eilcrite> 

V  s  «.p^  (  J,  iIq,  Crtfff*  IX. )  i  hic igitQf  «  ^  «—-4 
I»         '   '   "  .11*. 

&  fi  T^  I,  aritesf/R 

X4  ^^•iTlt 


fii     ,  SiSi§  II  c^ui  rtf. 


0b$  4U$mp&i^Umf  tf  imhiMtiow  dtfcribi  p^ 
aji  fuairii  $mvM  ^  qarv^is  enim  cum  ( ut  na« 
l^r  JniUr  Brtvwii  Afton, )  d^rerminamr  per 
CiKrtjm  iii  4^to  piincto  inflextonem ,  &i  p^f 
^usdtm  inflexirfnis  VAriartonem  iti  pnnAii 
ibquenribus  tuxra  determinatam  legem  j^  e.  c« 
fMirabaU  difierr  ab  ellipfi  per  Yariam  infle* 
Xloftem  in  verrice,  &  in  {^iiAi$  fequenti* 
IbuS»     Atqm  pr0  pmsprojc^tohu  ^  VF  grAViuHs 

mnMm$io9$$  pbteft »  imo  d^er .  habeH  v4rU$ 
m$rv0  infl^xi^  ram  in  verrice  t  quam  in  (e- 
^nentibus  punAis}  ergo.  Pr.m.  hoc  niajor^ 
•ut  minor  eft  infiexio  ilia »  feu  curvedo/quo 
Ihagis»  aut  minas  mobile  dede^cre  cegirur 
•  t^ngipnre;  vel  ab  iminobilt  cenrro  morustf 
S)ede4fttr  atirem  magis  ^  aut  minus  imo;  j^re 
msri^  fMPttiisio^  vis  ceHtripots ;  natn  quo  major 
tft  vis  centripecat  hoc  magis  rec^it  mobiI||< 
4  tang$Hi$i  Si  contra«  .  ido  t  pr^  PMria  velocim 
t4if  pro^hom^  quae  quo  minor  fuerit  ^  bo« 
itminqs  recedee  mobile  4  $$ntrp  moiui  Jnt »  8c 
Caatra.  Jtio  :/m  vm$tau  dngUorum^  mb  qui<# 
bus  yi$  cemripera  \  8c  vis  projedilis  conipi« 
r«0t^$  nam  fi  direAio  alteHus  ad  alterata 
fuerit  ad  adgulum  stuium^  iiabebitiir  acctflu$ 
mobiiis  ad  centrum  motus :  fi  ad  ohtuJum,  ha«  / 
bebitur  recefitis*  Ergo  com  in  infinitis  gra« 
dibus  rhafor  aur  minor  efTe  poflir  vis  centrr» 
p«M  relnle  «d  vim  proie&ionis  1  cumgue  di- 
'  ^erfi(fim«  habtri  poilint  (eu  virium  dtredioki 

tm  I  fta  projtftiteum  ceicriuueii  patei'  ru 


«•.  8tvemper4m »  &  eombinafis  virtbo^ .  illii 
l|uimvis  Curvedincm  h^eri  paiTi*  Nec^ 
-  mocto  in  vtrUc9  vdrla  .curvedo  obrinere  po» 
teft»  (ed.  &  in^mtSis  deincips  ftfitis  i,  ham  fi 
l«x  grdvimis  m  variis  a  ceotro  .diitanciif 
varia  fueri(|  naicetur  curvedo,  u(  Yoluerii^ 
varia, 

« 

$.  176.    S!  iiriWft  vis  tmHpiU  4d.  vim 
frtyiSionis  »  li  Vi  /  r#^m/  vtSltr  tusn  ungeru^ 
fstit  4ngulum  acmnm^  habttur  dcc^u  mcbilis'  sd 
€    trnm  virinm ;  nam  6t  L  t  diredio  t.^genij^ 
tis  C6g*?.9*)>  aflumpro  arcu  l,  B  iniimcefi^^. 
1110 1  du^isqje  reftii  C B,  6c  L  B  eric  tans; 
angulus  LCB »   quam  P  L p  infinicefimus^. 
ttterque  enim  evanefiitc  eb^unte  B  in  U    Eft^ 
vero  adhuc  acutus  angulus  CLiS  yUt^^et^ 
qul  idcirco  dato  aliquo  angulo  a  redo  d(fFe« 
voe;  proinde  ottam  actstus  erit  excernus  CBp^ 
iqoi  cum  aequatis  fit  duobus  interiits  oppou« 
tm  fimul  fumptiS)  ab  eo  difFert  per  inRnite« 
fiaium  L CB.    Erit  igit^r  CBL obtufus ,  fic 
latuf  CB^  quod  obvercicur  minori  angulo^ 
ii}ini]$  lacere  CL\  ergo  diftantia  imminuitur» 
fcecquo  immiouu  hwetur  accefilis  ad  ccn» 
tctim  virtum. 

^  n.   Slf  ridins  nt8ttr  tnm  ungmi^fscfsi  m^ 
^mm  chufunli^  bthctur  rtccffus  n  ccntra  Vitium^ 
oititcrumLF  dlredio  tangencis  ad  anguluovi 
o.bcufum  (fig«  40.)  i  du^a  CJS>  ULp  /^cu« 
|«»  paif  «liQiaa  ^bttiidat  arcuai  ^B^  oonfur» 


f99  StBh  IL  Ofm  Vtk 

snguti  ad  Bf  ScC  eront  jcnri ;  maius  taitar 
•ric  iacus  C  5,  quam  CL  ;  proindeqM  d«w 
ftantia  mobiiia  ao^a  fiec  receflbs  «  ceom 
Ttrium* 

JcAtf/.  Si  <|iiit  neget  fngalmii  CL  Jf  obrofiiai  elf 
ie ,  dDC»c«r  C O  pcrpcndtcokris  tdCLi  patebic  in» 
gulafo  BI^C  cooipooi  c^  O EC tt&o^  dc  B£Q 

acuco. 

♦  -  . . 

Ilf.  5f  railrfr/  rr^or  nir^  Ungtnu  cdntihef, 
sngfiium  r^fhp^ »  bJketur  jdm  wejjus ,  j^im  rrr«^^ 
/fc#  y  y^m  Jenuftti  difiantu  mcbiits  nt^ntt  l4Jifft\^ 
frontvilocitafprajcflionirfuerit  nnnfrtr^  vel  msjor^ 
Vfl  d^ualis  refpectu  ejus  veheittttis  ,  ^us  fer  Jimi* 
dium  dtfiantia  0  centro  'virium  itcauir&etur  vf^^ 
4ju£  ibi  6Aetut  in  curva,     Adl  proiedionis  -di- 

re<%ionemL?  ducator  parallela  JC^(fig«4i.)f 
Paret  imerr^Iio  CLTtribos  quibusdam  dtS^^ 
fcribi  pdffe  circulom  (  §♦  frdced.  )  ,  coM 
portio  (ie  L  n.  In  hoc  circulo^elocitas  eflfi^ 
debec  tatitay'  quantam  mtibile  acquireret  ca- 
dendo  mot^  untformiteraccelefato  eit  L  J>er 
dtmidium  radli  LC  (§•  I8s»  )  ;  effeftiH  au-i 
tem  yelociratis  a  fola  vt  tangcmiali  provc^ 
nientis  eo  tempore,  ouo  fbla  vt  graviratif* 
decurreretur  LX,  ti\Lir::i  Kn;  ergo  (%ire- 
locitas  fuertt  minor ,  ejus  effe^us  eodeis 
tempoftulo  ef it K  m,:=i  te\  fi  mafor ,  ciui 
^ffe^us  erit  JC«=  ^f^^viyindt  \n  primo 
cafn  puniftum  m  jacebtc  thfracirculojn',  eo« 
qne  tpfo  fmnuecor  dittaana  C  hf  ih  iiUero 
'  ^  cafu 


caitt  pniiAoni  •  iacebit  eietr«  xtrculam  ,  0ok 
que  ipfo  augetiicur  diftamia  illa  Cfi^  qurii9 
circulo  s:  CjU 

§«  1 77,  &  rsMut  vlf£lw  cuni-tjinffnu  famt 

luti  cnfiiu      Sit  EQ  rj0^a  (  fig.  42,)"^  qnam 
Corpu$  defcriberer  firfS^yr  proje^ili,  aot  pra?-^ 
cedenti  velocitate  p^^vfin  inertia?,    SiifF 
reda  ,   qiiam  corpusMeicriberet  unico  im« 
pulfu  yis  centrtpetse  pff  um^fculufn  infiHiufi'* 
mum  ordinis  />r|iwii.  v&i^'  dc|niguf  direAio  vis 
tangentiaU$ad.cent3S^peum  (ub  angulo  acu^ 
to«    Tum  dficaiur^  iA  perpendicuiaris  a4' 
£0:  cadet  puii^um  ikf  jultra  G\  quatfepor^. 
tto  G^  erit  infinite  parva^infinitaee  ejusdeoi 
ordinis ,  cuju$  tik  GH%  ad  quam  (e.  habec 
m  cofinus  anguli  H(?Af  ad  radium;  vei  cu« 
jus  efl:  HM ,  a4  quam  (e  habet  ut  ideiu  co« 
iinos  anguli  ^  (?  ad  co(imim  ejusded\  anguli., 
HOM.    Eft  aotem  <?H,  (ivc  i?F  infimtifima^ 
mniinii  JicunM  (  cum  fpatia  ab  ^mnibus  cor« 
poribus  libere  defcehdencibus  confe<Sa  (ine 
utquadrata  temporum ,  bic  vero  tempv(ca-»< 
lum  pcr  f^Bm  byipothfin  (ic  infinitcfimum  ordi*  .^ 
m  frimi)  i  quare  etianii  Q  M^  ScHM  erune  ' 
infioite(ima9  ordiinis  (ecuBdi.       Porro  (i  ra. 
dio  E  H  concipiatur  defcribt  circulus  ,  qui  . 
produAa:  E  0  occurrat  laN  S<,  n^  habebitur  * 
propoi^io  ?  Mni  MHr^x  MHx  MN  (  de» 
monflrant  enim  Qeometr^e ;  quod  |;ierpeu« 
dicularia  e  (}uovis  p«ri^)«rM  cir«ttlaris  pun«  ^ 


/ 


J99  SaklLGifMm, 

Ao  40O>tffA  ad  diamotrani  lit  media  propor^ 
ttOMlii*  tnter  (egmenta  diametri ) ;  fi  erg^o 
Mn  fit  infinitehma  primi  ordinis;  U  M  H 
inHnitelima  Tecundi  ordinis,  ericM/f  infin^ 

I      I         f       f 
ttfima  tflrtii  brdinis^quia  —  ;  —  ac  ^*^  s  — | 

ee    009      00»    oa? 
cumquo  pars  inBnitefiiha  terrii  ordinis  ne« 
gligi  poffit  f^elaciQ  ad  infinirefimam  fecundt 
ordinif,  ficut  infinitefimum  primi  ordinia 
negligi  potell  reiate  ad  finitum :  erit  GMc: 

Jam  S  0  defignat  velocitatem  pfiorif 
(•mptifculi ,  qu«  per  vim^inertia:  continuata 
airero  tempuurulo  eahtbet  Teloctrarem)  aut 
vim  projeAitem»  B  H  dofignat  yelocitatem 
altero  ilto  fiiquente  rempufeulo  geniram  vi^ 
ribus  EG^  8e  B  S  ;  proinde  eft  I  0  ad  Gl/^ 
iicm  velocitas  pscoaentis  ilempufculi  §d  f4 
imrmtmwm  (  tn  circulo  enim  radii  omnei 
iBlfjoanturs  ade)>que£/fs5  ^AT);  quarecuin 
prMedento  tempuCcolo  Velocitas  fuerit  fini« 
ta ,  ejiH  incrementum  tmpyfcuU  infimujhno  ■ 
^ikfrig  primi ,  erit  otiam  iitfmteltmum  wiinis^ 
frimi.  Sique  in  polygono »  quod  evane^ 
ioentibus  teniipbrum  intervalKs  ,  &  figurx 
laci^rijbus  in  cuivam  conrtnuam  abic ,  fifHta 
iHfi$  tmfvn ,  angulus  fiierit  acotus ,  veloci* 
taris  incromentum  tfhfinitum^  quod  cum 
negligi  non  poiSt ,  dicendum  ;  viribui  sJl 
Mff$lwn,  4iiu$um  m/finmUkks  vitociuum  m$Mii 
in^fum/ti  mrvn  r$vm$i  pr^mrh 

Sio$L 


X  / 


-*•.«'      t   ■  ^ 


'Sd^dA  Ne ,  oro »  monflra  ^ptitn  in  eerebrir 
fto  depingit  Tyro  «Qdirit  fbcilmf  :  ii^mtttfifnm  of\ 
iink  pritni  »  §M  ftcundi  ,  vel  ttniU  Portio  infioitt 
perva  finits  quenntetii  ,  dicicor  tu/MtffimA  ord^mt 
fritm*  .Huius  infiaitefimc  pars  ifcrom  ijifiiiitefiin^ 
dicitur  infiniu/tma  oriiuis  fecundL  Iflios  tindeoi  it» 
rum  iniinicefitni  alii  nancopatur  infiniufimu  ttrtii  «r* 
iinh»  Exemplii  i  thefiioro,  vel  mari,  vc)  priegranA 
di  monte  pctitii  ^  fic  commode  iftnd  ttloilreri  potcft; 

0  •  •       • 

r 

,  IL  Si  raditu  u8or  cim  ttngmujAciju  mt^ 
jpthtm  ^tujum  9  totoHtas  dscrcfcit.     Datii ,  ut 

firius  9  redis  £  G  ,  &  £f »  fit  direaio  itte* 
ius  ad  alteram  fub  angulo  obtafo  (6g*43«)* 
Si  duQetur  HM  perpendicularis  ud  EQj  ca^ 
det  ipun^um  Af  citra.C;  quare  GM^ric  de* 
nuo  infiniecfima  ejusdieni  ordinis  »  ac  0  H» 
htHlA\  cbmque  GH  fit  infinitefima  lecttn<^ 
di  ordinis ,  emm  GM^  &i/itf  infiniteiinM 
ordjnis  (ecundi.  efife  deber«  Deouo  ccntro 
J^,  intervallo  AH^  deftribsitur  circulus  tran«*: 
fiens  per  punAa  2Y »  &  n  ;  fietque  M  n  t 
M  H  si^MU  i  MNi  ubi  rurrum  M  N  erit 
tnfinitefinu  ter tii  wdinis  (  iisdetn  plane  di 
cauffis  9  quas  .iiipra  recitavi ) ;  (iromde  M» 
gled^p  MH^  adbuc  manebit  GN  infinitefimua 
ordinis  (ecundf«  ^  Eft  autem  hoc  loco  GJf 
i$er$9»t€tutm  velocitatis  prstcedentis  ^  quod 
UnMiftulo  ittfimt$finm  9rdini$  primi  &  ipfiim  ti^ 
it^ttiufnmt9$  ordMs  frimi  f  iMoqisc  tempu(ibu« 
ki  fttiip  fbAum  )  quod  cum  Mg^igendum 
aiaii  fit^  ftatutndwn  i  Si  in  p^ffiptm^  mti  iut^ 
M  ifimtii  tsMtn  V9lkr  mm  ungkukti^  mtgSi 

htm  shtttSatn^  ngi^iig^tm^  mt^ilu  JmfOkmOm 


c 


IS4  StakJlOfmVtL 

IIL  Si  ndbi  Mflbr  emm  unpm  tfdti 
jpdtm  r^Sum  %  vd§cHsf  mMh  t^^imiuar  9^im 
farpnftrm.      Cxreris  ac  (bpra  poiitis  videbif 

{lerpendicalaretn  HM  C  fig*  44« )  cadere  itl 
pdim  Q\  qaare  G  M  przienie  cafii  erie  nnl* 
]a)  fed  HM  €tU  infinirefiiBa  ordinis  (ecan« 
ci  I  iicuc  E  F*      Dudo  rurXum  circuio  fiec 
Mmi  MHss:  MHi  MN\  ubi  Af 2f  tft  aafi^ 
tiicefime  rerrit  ordinis  j   quare  ScGHp  qu« 
prnfrus  eadem  eftcumM2/^  manebicinfinU 
f e0rrta  tertii  ordints.     Quia  vero  G  Jtt  cxhu 
ber  incrementum   velocifaris    praec(^dentis  | 
^oir  finita  fdr^  Incrementum  itlud ,  ^ipipv)^ 
U  injiHitefimo  primi  ordinis  hCtwttk »  orit  inffiim^ 
Jimum  JuunM  ordinis  f  Umporc  autem  flnHt  ac« 
ceprum  >  erlt  infimufmum  primi  ordinis^  quod 
f  efate  ad  quanritatcm  finitam  negligi  potefi; 
Crgo  /t  dircSio  ungtntis   ad  rddium  v^Borom 
Jherit  pib  M^uJo  rtao  ^   ulociUu  mobiUs  $4dt0 
J^irpttrdit. 

>  *  StloL  tiide  fidl#  emihtf  (otnlie  prohtmaA  ]flk 
^icntii  I  Onormiiuure  uhrisatit  imrwtintum  f  vd  4t^ 
tttm»fnium  fingulis  ttmfufaUif*  Nafn.fi  dtcafttr  CtJ^ 
(  fpetiutn  I  qood  priore  tctnpuicQlo  confcfiom  fttjr  | 
tf^  S'y(\  temptt(culocn  sbs  T;  tderiras  proxtmo  fetn^ 
|n(cHlo  habita  a  C ;  «jus  iticitoicYitum  ^  vsl  dccrc« 

iDintttm  as  c  ;  vls  autifn  p  Vi  qitti  (WimcrTtf '  ^ 


1,1         .*  *   ^^ 


^ AT;  MtirmUm.  U  Jiuim«mfkmi«it>ttigdi  H Ghfi 

,,     .  FSS 

cc 

f  «fi ^  «ta«^  I  i,g,i  ij^i  '•   . «,      Porro  cum  £  G  defft 
V       'j   CC  CC 

gitet.  .fp^tiDiii  ^Dre  ttmpQfcuIo  coftfcftmn  ^  &  0  N^ 
icdl^G  4^increaieutQm  ,  l:el  deercmcmum  (parii  (  ini^ 
tK^ctpc^li^;^  (|^tii4cm  fig^  49.  i  Tcd  decrcmcntum  fig, 
4}^ ) ,  jerlr  fpatitim  £G.id  fui  incrcm^uum,  vcl  de^ 
crcmi^ntum  ^  ficut  ccleri('as  ^d  fm  incrcm^ntum  ,  vcl 

"   *•  *—  :     nyss  ynVS    \ 

^  itertftieniam  i  Hi^tSi  ■■■ir."  »  .Mit-a  C^  w ■  j 

3  i      -      f  ..  ..V  >    •  CC  *    C 

«trgo  * s3    :■.■  «      Deniqoe  ;  cum  ^  s   3^ 

liilMfisr  #  £3  II  ^71  h<.4i  ifnremint^  ^  tac/  i/itt4b 
qoonf&  .fangook  tffidt  enm  dijrettQM»tie  g  A  «t  imi 

-"     $«  t78«  Theoru  .irifititti  tfMtraikitti  f  tn 

qiiaounqoe  com  iiicedtt  tnobile » -fiehaber  i 

.  9  c^pus  juxtM  dhiSthnem  quimcuHqUi  projtBm^ 

fimul  urgiitur  finffilii  tmpufiulU  Ver/us  punHunt 

^i4ffd  iXtra  pi^offjSionu  air$^on0n  go^um  0  di^ 

i      prilft.t^  ^  iatirs    iifj^$m   polygmi^  (  njgi  4$«  >,i 

W  Projifiatiir  otiim^  «offui»  e^^in  B  p  iut  ihs 
chifo:  fefi>pMn;iilo  decurrec  ABf  fimttiqde.eo^ 
detii^'«em  pufcuto  orgeer ur  vi  ctntf\pnv  Tor^ 
fiif C»  fic  tatnerli  ut  eoden^  iHtf  (eMpafeifttf 
foU  vi  grayiUttt  1it>ptti(isii  delfujrrcirtf  W  D\ 


§10       Mhtt,  efmm    ' 

corpos  hit  ex  A  wg^biMt  Aatb^minkm^ 
quariim  dir«AiiiMi  AB^  AJO^  quire  molia 
compofieo  deftribet  didgoiulem  A  M.  St  ia 
fine  prtmi  tempu&ult  cefTifet  ^6t\o  vis  cefi* 
tripetj^ »  (ecundo  rqutli  tcmparculo  corpm 
fuld  vi  inertiss  abirec  per  SG  s^  A  Et^  &d 
pomrur  non  ceflare »  poilttur  iterulii  corpiii 
ur^erl  vcrfus  C  iiixta  diroaiooem  E  F  }  pro» 
inde  iterum  def^rribet  diagonaicm  E  H%  Sf^ 
militer  terrio  tentpuicolo  lola  vi  inortis  abi^ 
ret  per  HX=t  £H  i  9f  ibla  vi  centripeto 
ptr  /f  i;  iterum  ergo  motu  compbfito  fpre* 
tarper  HU  .£t  fi^  tempfiftub  410  perL<4 
5  to  per  0  it  &C,  5ed  bm  diagonalos  ralciaiie 
polygonum }  ergo«,  % 


• 


StM.  Cooci^itur  hle  irb  centtipets  ( 
JbdtmfMttf  )  ageiis  per  ftittirvalts  tiiitki  6iigaloroot 
Isflipoftaloriifii  oqosliiiln  \  ^oo  initto  ffodacat  lioiol 
satam  «sm  vsioeitatetti »  qoim  aftiooe  eontiflas  par 
totmn  ijpfliai  ttmpiiiculiim  prodtoccrct  >  'qoo  fmdhm 
csAi  dcleribitor  polygoniim  quoddsm ,  iit  dcinde  im« 
Mnotii  inttff dwi  tn .  infitticoni  ^  doDce  peoitds  ava* 
Otftat » .avaiw.lctiitfta#  fimoi  kccnt^us  poiygom  ba» 
bsator  aorvatQra  cootiooa  or^  ax  continuo  ^  A  ios 
4(rfioaid  impolio  vis  ccocripftf » 

CpHtH  t  Sl  lcmt>ti(ctiU  »  ft  polji^Mii  Istcfi 
fttacipiaotor  iofiliht  psrvs »  its  ot  ndmettti  eoniiii 
Moiw  aMstm^  >  ibagnitudd  auitom  ^fiiiita  oiitrtia* 
lor ,  it  afio  fta  esmriptto  fit  contlnoa  1  tmo  modo 
fri||OOom  sUhk  in  ctrvam  Ui^c^  ^  icd  *  dktlUtl 
fia  ifOjsiiHi  tvadat  lu>c  Csjtl^  tsogcos  eurfo  (  iisoi 

{fodMcantf  hfaa  Mddvii  inhmti  jf^tvtm  0  ITJtt  S^ 
tT|  liMMitei  |ti^  Ofit]  mSfuiigm  m^ 


^ 


P$l  moi^f^  hifplit  %i^ 

t« .;.  btbctiit  eniai  i^roprieutei^  m^jfAii^  .qti9  ^  ^ 

ijit  fit  reHa  omnmn  pro^ima  arati  ^  ita  f  ut  iuf$r 
eam^  ^  arcum  alia  nQa  ductnm  fofftt  ^^fid  aliqua 
Jpilnm  Jiti  f^rte  imwergaiur  intra  atrvihn  \  unde  ttiark 
ionfequitnrihiitam  ejje  tangendient  cnrvte  dat4t  in  dam 
Ifuaw  fUfiScjf^  cn^  jfimVmrn  uuica  tantummad^pr^^i* 

CoreB*  IL  f  olygoni  lateribut  infinite  pinris  Cvh- 
^taii  JpifSf^  tn  i^rignecro  arciif  infinite  panri  ii«^ 
^m  r^opdencest.  Qasconque  igiciur  de  iftis  ^ica^. 
/U  bit  <]aoqu€  intclkdt  volo .,  cam  nihil  diflT^ranc  a^ 

CoraU*  llt  'Dum  mobilc  per  poly^omim  incc^ 
^^  cx^^  tfViot$srCtir..ih  £ »  dcfcrtbit  radio  tfedorc 
fuream  ^li  ACE  (radium  enim  ueBorem  ;;ppcllo  lino^ 
/iC^  vcl  £C  a  CfDtTO  motut  dnQam  ad  iliod  orbic# 
poDdum  9  in  qoo  mobile  cxi^jr }  #  •  $hnili|cX'  ^rgo  fi 
mobilc  in  pcrt^necrQ  curvir  fisiuicap^sc  inccdac  ^  j^ 
fcribcc  radio  vcAbrc  aream  ftfiorit^^^C£  (  nam  Jj^* 
fttrem  vffco  partcm  vvM  CQUiftfi^W^m  daoboi  f^ 
"*t,  &axca).  •  "     .    »tj     ^ 


Iro  ki€$dim  dffirm  rsJk  vpMmt^fmMhttJem* 

"jtorius  squtitt  ittdt.  Dim:  1n  fig* '  pfyti^^^Ia 
ACB,  £CH,  HCL8cc/mtt^ti\hlttiAn 

«inio :  AW  ACE  atquatttr  £^\q  £CG(qam 
habent  «quaUm  bafim ,  fiC/^titadjnem  ^  fi 
enifjf)  per  C  concipiatur^qgi;  pacaU/ela-^ 
if  Gf  >  lacebpnc  ambo  snce^  €M>dei»  |iairaHf* 

'  las ;  ergc^babom  eandenr  altttiKiiiieiis ;  tom 
qoiaii£:=:  BG^  babent  fmriliteiM eanchttn 

'  bafim  }  •    Porro  i^lom  £C(/  ?s  ifilo  g  CH 

y  '     (ma- 


1 

C fHanentti  «fttm' cadem  bifi  f  Chabe'neVtn« 
aetnaltitaditienv,   cum  linr  inter  e«ide(^' 

jCSzx  ECH,.  P«ri  r^tione  dAnionftrJbis* 
£^]M,,HCt  ^LCOyOCR  xqu»li«  tiXt^  Sed  ^ 
ha»c  ^la  iiint  are«  xqtMliba»  CMnportbu^  d«» 
ear&5  ergo. 

'      5c]&d/.  V  Theofema  Iftudi  qtiod  cYim  ftqtienil 

-Corollvio  Regula  prima  Kepiertana  dtiitur  ,  eft  pcit* 

Cipuanr  Aftronoinise  l^byficse  fbndaincntcni  t    altuiil 

|ih>ind:b"' ^imo  defigenda'  dw;t\  adjun.£lii$   Coroiitrili 

OltiniBus  j'  qiiorum  inaxiinus  ufus.crit. .      ~ 

5<s5b7?  Jf.  Facilfcft  demoflftrarc  Inverfum  (fte^ 
ireina  :  Si  tnobik  in  fofygoni  ftrimetro  incedeus  ^qrta* 
ilbm  temporrhiis  dfjcrihat  Mfeat  aqUilet ,  mrgebitnr  vh 
'iribus  'ttd  iderntHiirHm  cdmfmrie  t^dintUm.  f^ift^ 
j|>fpdlaca^ttr  // E  inO  (fg.  prac.  )  fic,  ut  ^£-s  jPG> 
Fiet  ECO  =i  EC/f  ;  proindc  ss  ECH.  Cntn^^€ 
V\'*  hgcbafim  habeam  *qtidlett* ,  cfunt  ejusdem  tK 
tlhidiiiis ,  h.  e.  crunt  inter  casdem  paralletas ,  cotifif* 
^uenter  G  H  parallela  E  C  Jam  (i  ducatur  HF  pm* 
f^U\iC\pR  £G,  bQbeUtur  itiotui  per  £ //  re&IoTu^ 
81  dttdr.alios  i  ^Hiect  per  £  G ,  qui  provcnic  i  M 
IrtertiiB  I  dt  per  B  F  /  qni  oricor  a  vi  leRdcnce  ia 
.  cerit^m  C«    Pro  firqaeniitul  ^lis  eadcm  «ft  demon* 

.1trati0« 

» ■ 

'  *  '  Cor^S.  Jt.  'Arta^  qtiM  vetrii  r^itU  veSor  ,  ftm$ 
^emparAus  ptopoftioUatet.  Si  cnim  rddius  vcdpr  «« 
qtuflif^at  tcqinporibus  dcfcrlbit  arcas  cquale$  ,  daplo 
'^tctnpore  Y^r^^u^^t^et  duplas  ,  triplo  triplas  ,  atque  iCa 
Icmper~ar««  tnint  at  tcmpora^  h«  c*  tcmporibus  pr9« 


-i*      ,  *  /  i 


Ortff. 


pimmk^HA^,        }^> 


<*-  ;  A^&Tt,  Etiath  w-ptti  in  kiifmiJl^Mr^tfeiHI^ 


^JiiifiiieHt.  defiribit  ^tquiUiita  i^mparUfUS  mifuitki  il» 

ttekifmtM  in  Mlia  ^u&vit(^nt  ffi  ffUi  hm  ai  ijfiti 
iglikil.'  Niiii  ^uiflk  otnhia  Utcn  tfjuiihm^  ]pt>fy^nii 
^qaalAus  lemj^cnlii^ccuminnirj  cft  Cit  it  Si  t 

trgoCjta  jLiA       •     , 


\  ^ 


ft*oji^onts  ptimx  ;  quacuii(j;u«  cnjiti.iUi  fit,  fitHipfft 
irelocicas  lu  quovis  latere  mnttbiitur  in  eiadeni  Mitt» 
M  /io-  qu«  nia(at|ir  ydolSttaf'  ia  latcre  prU&llft 

•ii^  ettjmd^  ffriwHtro  moti  iehtti^a^  4n  ilivif^ 
mHNi^  pimnQis  fitm  iu^irfi  wo  porpiitScuU  m  mtrf^ 

k.tv  hoe  aidk|or-^ric  cderitift'.iliehiiti  ^.  Jim  mttuii 
]ierDehdie|tlaiti  ^  fln^ciflimir  Vi^v  S^i  t  iA  «^a 
dcitrihtt  «taditt»  irtftpr  «quiriibUs.lftiipMdbta]^  «quidc* 
irta^i^  SMeJam.  dbD  tetnpliiktiia/qboirum  altcro  K#i 
dbi  Vtjtoif  de^Ht^atf^liOti,  ap  »1  icb|bl  dtltti^  Voc«^ 
liir  «^i.bi&l  6i  idi^t^J^ltitii  ;^)  tujui^titudl^  i» 

■  • .  •         -'    *^  .  ,^4$  t*    . 

UI»  «I      fltt  piilr  MlHilii  k  m  te^ic^a  >^  V 

I  i 

UV«ndo  in  prbportiotiem  tiJbtiti«bktil^fit^.«Bi  ii  ^ 
toiif  Vero  attttuiint»  Ipfil  pK^ytfndictilt )  .bhfts  ittltm 

iihiilMnc  (palM  t^oaKbtti  tfmporlkot  ctiiftAi  ^<)tM| 


Iqt  lB0|D.;|qiiibilt  lEant  ot  cderttJitcs  ; 
iJMtla , 'qoani  cdcriutcf  fiinc  inver(c  ot  r^.,^, 

Mreviteri  jqau  vf  £  ,  &  £  //  pcrcorrootur    , 

tcnipQrc  (fig,  praced^  )  lubctor  /^lom  A  C  Z  ssl 
£CH ;  tn  /^lit  iotcoi  #qiMltbu#  ba&s  (imt  rccipro- 
coiK  altitodincs,  ico  pcrpcndicoh  f  ftr  G#9w».^^ 
mtpAEi  E  U  ^  EC:  A  C  Sidf.  hiqwAE^ 
&£Wdenoiont  4>*tia  codem  tcmporc  dccorfii,  pro« 
indof^iic  ^cclcriiius  \,  EC ^  6i  A  C  fiippopontor  cflii^ 
^MH^P^  ;  crg9..  X>%x  ;  folooi  tn  moto  atqoabi^ 
li ,  \\T  ::^  r ,  Ipatia  fant  ot  celcricaty  ;  atqoi  tm% 
m  qoavis  cona  ,  domaxat  in  circaiari  habctar  motos 
•W^fiif  i:  eigo.  ^.'  ^ioacanqoe  \%fjB  acceleretar  , 
0|U  r^pvdcturoioioa  tcmpufcmo  infniu  ptrvQ^  fcinpcff 
f  191  «qiialiiU  babcri  potcft  ,(  ^  17}. )  •    ^ 

&ioA  If^«  Dixi :  cclcritatcs  fant  invcrfe ,  ot  per* 

rfidicok  ad  rangcmct,  jfjpav  erit ,  prdiutlm  fkmiC' 
;  (imt  cnim  in  ^tis  cqQaUboa  ha(cs  onivcrfr  o» 
MnUUms  f  qoif  «noiinwr  perpendictititM  Hinc  celefi*» 
iia  iil  ^ovii  ptiitQo.l.'efiiidem  curvs  ,  cft  in  ratioiw 
fictprocc  perpendicoK  C  f  e  ceniro  viriom  doeU  iii 
Ciaigiotcin  SLT  (Bg^  47-  )  crioHeoniem.  per  ip&inf 
tMfiiHQ  t ;  mm  iotim  in  rationc  iovlrfi  radii  vcdo* 
tkCL. 

'^*  CorcV.  V.  Si  T  ss  # ,  eeleritatei  ecrporie  ht  eifi 
€uU  ineti  itbique  fnnt  ^eauaUs»  ^  In  circulo  enim  x^ 
qoamor  radii  oipnes ;  mi  vero  (unr  perpendicula  a 
cci^irp  flgiirc  id  tangentc a  dcmifla  (  per  Qe$m. )  « 

CercU.  VL  Sinon  babctur  T  zi  t^  aut  fi  gem* 
mXimr  moent  ht  ooa  eurtfa  cot^ereftdm  fit  etm  niotit  im 
/ptavie  oAo  <etrvat  eekritatei  cerporif  inpolygom^  vel 
fmrvte  eafftnva  perimetro  moti  fuut  iu  ratioue  cemp^ 

00  CM  iMrcAo  meeknfi ,  if  inmf$  p$rf^iisi»hmif^ 

Detn, 


^ 


t 

Dem.  Sint  priora  dno  A'^*^  =»  — — ,  &jr  8 


"^4 


•«rgo  a  *  a  -4B,  A  a>  r:  «* t|.  i.  ax.  VI  )  t  ^fdb 
inde  B  rz:  — — ,  &^  s;  ~s  i    ^C  4^**  IfiBpIii  thiit 

ut  dup!«,  fict^-  ,  *  *  r:4  *-^;  (cofl%ii^ 

X  y 

•ter  Bs  *ss  —  t  T**    Q»**D*  ntmB,  ftl^ik^ 

ttnt  celtritates ;  x  Qny  fiint  /l^la  ,  ftn  alres'  Alonmt 
Tadio  vedore  detcriptorQm  ;'A  6^  a  iiint  «Itittidtnei^ 

iqnaa  ferfiHdieulif  fliccimMr  ;  dcnfffoe  fraOionte  rrsj 

y  ■•  '  •'    '^ 

<&  — ^  liidtcanr  rattonenr  eompofitam  ex  dtfidi*lif« 

-         •  *  t- 

^eolaram ,  &  inverfil  altitadinnm* 

CcroV.  I^IJ.  TfMfav  pfrhdfcnm  m^ittk  HH  M^ 
tuniju0  atrv0  inefieutk  efidireSe  ut  aren  erhi^  hiugri 
defirihndit  ffinverji  ut  ureaSeOerif  tempare  .dat^M 
feriptiJ  Com  entoi  radios  vedor  «qualds  areai  verrae 
cquialibQs  tempoflbas,  tcmpus  integr^  revolationft 
eo  mifas  efle  debet ,  qoo  majdr  eft  orbis  integri  areC 
&  minor^iHina  |lortid  datc^tcfiipore  de(cribitar«  Bri 
nnar.  Aflren* .  Si  ergo  tempua  tllod  dicatnr  7«  «rMI 

orbis  Integri  A^  t^QmrS^  erit  7  ss  ~  •    h*  l^iTt  t 

a      •       ^ 

A      ^ai      -^  'if  •   V 
tei  ^  9  ^lfr%\Mi^Tt  0  ^  A$9  aSi  « 

S      ^i  •  .      , 

y }  S^ 


ji4*        pBkn.  Ofawn. 


x^ 


^  SeM^  F.  Jorim  daariiuoi  htc  expofiran  cx 
Jlo  itlnflri  a  iliotfe^  QBia  radips  rcdor  ddpribii 
tro^  ccnporilntt  proporrionalet ,  facile  coilficies  2  il- 
Jm|  cflf  Cfnrrmn  inotqi .  circa  qood  ares  teaiporilktt 
jprdlportionales  ^cAribi|n(Qr.  '  Tales  defcribit  Laas 
prtM  Kmm  ^  fi^t^  yovi^irc^  Jorem ;  ftrrM  igi« 
inr  eft  cenernm ,  in  qngd  rendit  Xon^  i  jf^n^  i  in 
^nod  firellttes«    Tooi  rede  aQrmareris  :  Ji  qnis  ph> 

^  jfOiarom  tdeoi  icbims  tii»endir  a  i  pr^grcdiendani  ^ 
^t  iil  C»  qaod  ex  «  in  /f ,  ar^s  Aflronoaiicas  ^Cl^ 
fCH  «qQaieacde;  caTO  ramcn,  inr^ras:  ergo  (pa« 
tic »  4(  cdericares  ^%m  c^q^aa,    ^rc«  co4eoi  tcmpo* 

.  fO  coofeSbr  nofi  defignant  (p^ia  ,  nfqoe  cclerirarcf, 
4mmo  «  91VC  M^di  afC ia  sqoaKbos  c^elericates  fuiu 
iarcrft  qc  perpeqdicoHi ,  fi^  Ofgues  9  ergOt  quo  Plan^ 
\|%  cft  Soli  ranquam  eentro  £uo  vicinior  i  hoc  jHajcir  eft 

lUiaa  cclcritas ;  mq  remorior  »  lioc  mUior  rcloQimi 
Vdo  ;  crgo  fl  naneci  revolratur  in  ellipfi  A  B^B 
#  ^«  46.  )a  maximam  cclerirarem  obtinebit  in  ^ ,  obi 

^tboet  mwiiMm  didai  a  foco  <  mitHimRi  m  vf  7 

.  9icdiam  in  £  d^  D 1  bie  cnim  Planeta  obtinfc  mr« 
4iKcm  ajhtmnm  (  ^m  .idcireo  fw^i^  dicitiir »  qatt  0 

,  W  ccmro  jijptr^  crigatur  perpcndicuiaris  ellipn  oc« 

*.  facrmn  tn  E^  tom  a  ^  foco  dapafar  i?  F,  iii^ 
i(  £  f(|  mtdi^  4lrmbiu^c9  mrer  maximam'»  &  mmi» 
«lam  PUmt«  diflanitam  a  Sole,  -.  Haio  rcrponc^t  cc» 
lcrinii  inedia  J  ^  lllrio  «-  crgo  qaa  pc<4»6nionc  Planc« 
fa  in  cUipii  rcvolatoi  dc&cudir^c  ponQo  w#ad  F| 
lltCi  cA  ifffii^Jumm  04  m^mt  ciAem  prop^rtioac 
lempcr  majoa  fpariam  pcrcorrit  codcm  rcmporc  1 
jjuno  A  in  pan£)p  <^ano  v#g«  mtnato  pcrcarric  crcaiv 

^Bt  dchnis  ad  pandam  B  imo  ftiam  mtnato  eon« 

$^  mm  fi  Ci  4l  iongilMo  itcai  imi  crii  «4 
longiradinam  idi,  ue  pcrpeiidical^ria  a  Soic  dqAc 
in  lanffcnrim  ircai  tdi  ^d  iliam  ircim  imi  i  nam 
irQ#  4f5B,t  (k  Atf  C.codrm  nmporo  dc6?ripta?  ront 
•fuilii  j  orgo  i}iHmittm  liiiciKlo  Iprimi  ^li  fiQ^erat 

ilH- 


I  '  ' 

^alrifudincin  (ccundt  ,  tfttitmidfin  b|iC|,,«4i  (jbptrtrf 
Mcb^r  badiii  tmi,  uc  h(K:  pado  fiat  .cooipen(atia.^& 
/\Ia  rc^Mcanru^  ftd  arqoaUratein»  IVco  t  crgo '^  qtt 
^proportio.ne  Pkneta  defecndit  ^  cideni '  propprHdt^ 
crcfcit  cdcritaa  (  crcf<iunt  cnim  ^atia^eodcm  tcfiipv 
rc  confcfli  )  }.  &  'comra  /  qua  proporciofic'  (llne|| 
•rccndit,,  cadcm  'dccrcfclt  cclcritaf,  ^ 

De  motu  ih  circulb;  .    ;^; 

*  ,»  .  ■        . 

§.  1 80,  Oir  corpus  in  9rUu  cirmJmi  mp^ 
vc^tur :,  Mimsri'  Met  lemims  virih^s  :  IM^II* 
'  ^fWf ,  &*  ccHtriMaf  vn  Mdtunquc^iiUa^buic  si^ 
'^ufeHinui  id  toim  ta  (imneifn  curvam  l[ 
^quiri  ,  alias  di^um  eft  )|  ^fi«/'  tmin^jic  l^ 
tPHPcrari  oportit  |  »1  vsIoHt^  Wfortj  in  cir^^ 
inctdcntis  ulHfsc  mamdt  c$4$m^  ac^unjifprsf^p 
Kamicam  in  ^ujusvis  eraieAofia»  puti^i)) 
quovis  ccletitater  fint  inircVie  ut  per{3cndi» 

\  fSoU  »  ^rpendfcuU  aatem  (  qn^  fimt  ipQ 
raUi)  in  ^ircuto  omnia  liqt  «cjualia  j  etiati^ 
yHocuatc^  in  quibu$cunqu>  cirgfili  j^^^S\% 
i|ire  debent  ^^uales  i  Hhid  yero  a  p^ha  lUf 
f\\xm  attemp^ecaiione  pendere  ex  cioouw)^ 

t  diceDdii  Hiamfeftum  fier* 

1  t  •  » 

/  .  $,  t%ii  Vic  $ltir§  iiuiram  ntfn/jwm  ^JJ^^ 
tkcvii  lAiim  corpus  aiK  ^iA  vi  centripeta 
§b\jfit  per  cangentehii  |  aut  ^ifa  vt  prpjv^^iH 
raec  in  centrum*  '  '/" 

$.  183.  Vk  e$n»iftf  .M proifSikm  ttUut 

*  Y  4  -        f), 


•  4  •« 


144  •^hV.  CajputVn. 

i^.^  Atiz  MB^vm  proitAilem ,  tum  L  M 
yim  centripebam,  Invenierut-  MB  efTe  me* 
jdiadi  proporcicinalem  inter  iWD, &  AfL  5-  at* 
guiifjB  eft  infiivfe  parva  refpedu  jtfD  j  er«* 
go  tfCiaiii  L  A^  refpedu  M£  ^::^'  if  L. 

$.183.  DinHiimif  vis  projeBHis ,  6^  5«* 
. -.  l^^^/^^^^ii^  #«y5«i/o  r«5^;  fac  enirn, 
confpirent  fiib  angnlo  aciuo  ,  crefcct  ^eloci- 
ta$  corporis  ii>  ci.rcalo  mori  jjconfpirent  fiib 
an^illo  obrurp  ,  decrercct  ( |.  ;  77. ) .  ado  : 
ttbi  diri^i^io  yis  tancrentialis  ad  ccntrafcm  elj 
Iplb  angulo  acuto  ^,  habetiiV  acccflus  corporis 
id  Centrum  virium  ;  ubi  fub  angylo  obtufb^ 
habetof  receflus  ($,.  17$.  3  •  Dtriimqbe  ad* 
yerfatur  motui  circufari ,  in  ^uo  &  velocita* 
ttbique  effe  debet'uriiform.is^  &  diftantii 
Corporis  a  centr4  in^nere  ea^em* 

$;  184*  f^ts%ntripeta  ep  Jebet  in  fMoH$ 
iompofitf'  ex  Jireiis  Jluplicata  eeleritafumjf  ff  /«• 
verji  fimpUee  radiorum^  vef  ut  afii  effferuntj 
iris  eentr^eta  efi  ui  ^uaJratum  e^Utiiatiif^appUU^ 
9um  ad  radium  (five  divifum  per  radium  cir- 
culi ) .      Quare  fi  vis  gravifatis  dlcetur  ^t 

•  CC 
ceferitas  C,  radiui/i;  fietr^s  -r-t    ^^      4 

$U  mobilo  \n  qubvJj  peripher i»  circulirii 
PMnao  B  (  %  48. ) ,  quod  vl  projeaili  J&  f , 
&  bontnpMa  tf  9  iriSputruiti  deicribat  «rcum 

»ii  qui  fi  •flbnucur  t n8ttiir  pkrvus '  «^ 

.     ■  dif- 


€i(fert  a  chord^*  Jam  ex  E  demittatar  peiy 
pendicularis  ^G^  erit  /i)um  GEB  ^^JBG^ 
^  quia  fi  n  veriice  anguli  redi  ad  hyporhei» 
nu(am  deinttctaci»r  pefperUlicttUrii  ,  divitfit 
M  Al^im  in  due  alni  tiaiii  «toii ,  qutnr  flb^ 
ffiuttld  (iinilia)  .  Conferetide  tatera^  hotno« 
loga  &etCB  yS  Bt::z  EBi  G  B  i  proind<| 

'  '  '  EB^    '*'*''..."..' 
6B  :si    ■  Atqui  veroGB  deHgnat 

srim  Cfmripetatn  ;  ^BB  «(b  Q>itiiim ,  tff^^pn^ 
indeaelMrti  (  nam  i  ar  »  t,  eft  C;^  =» 

CC 
&•/)}  CJJeft  radius;  ergo  T  =3  — -. 

^'  Or«i!^  It  '  ^  il  cll  finus  ver(as  arctis  B  £!  infioite 
parvifcft  pnim  p«rs  j^adii  imfiseepta  inter  ICbQipi  x^ 
j^uni  E  G »  &  arcam  £  j9  j( ;  Vgv  j&sy  verjm  maimr 
fim  cemripetam.^  rj    •  r  ;-^ 

OroU.  U.  I  Biaeqi  vis  cVntrtpett  ^  fitt  vis  gravif 

Aa 

Mtis  s5  ~-  Xi  «^J-  CereJUlVAi  hic  vcrocadcni 

1      "    ccy  M  .. ' 

gravitalk  =3  .l-^i  ergo  (per  #«•  IV.  C,  i.  J  r-^  cl 
D  DJi 

CC  CCDD 

-^'^   CCD  (  fer  ax.  Vt 


'\ 


't)Jh  .       D 

f.  t.l.  HStte  paret  <  <^4  ^tatitate  torporU  tfret 
t!iu4  gyriaHf ,'  (^mfut  Mli»09  •  etttm  mem,  ttgn»» 
fim(MmtttMrv,.t$tratiHi, 


SiSkMr  C^<  IHf^ 


ette,  fie  eom^convinces  :  arcot  £  ^  ponlcor  infintte 
fAttm ;'  ergo.eckm  tngiilQS  ECB^  mjos  menfora  A 
EB>f  Ifft  infinitt  peiiivi»  ,  qoi  li  negtiga^Qr  (  negligjE 
otnm  poteft  infinirtfms }  ,  erqu  «iigoH  C  EB  ,  dt 
Cii  £'4in»o^  fiioipti  #qpalft  doojbos  opftis  ,  com  a»- 
josyvi  A^  oipn^  tWHli  (imol  (bmpti  ad«qoenr  dnoe 
te^o%pir  Gemn  ,  Forro  iir^lo'lfi)ftclcs  sngnli  ii4 
iafim  fafit  ^qoales  ;  hie  CBEi   ac 

'proin4e  oterqpt  rt^oSt' 

Obtter  innoo  t  eb  etndem  IMhtum  panrlta* 
tei»|M«ili  C  (fig.45;)  Bn^s  vf  C,  6cfiCi)ofle  iC 
iiiaii  ot  pafrplieli^  ;  naip  iqmodo  ai^otii^oo  imerin 
td  candtfD  partem  oppofiti  adxqoant  doos  rcdos^  lior 
betor  ptrall(li(ipi  eriti^Hoil|«  -^       r :  T 


(;■ 


ScUkU.   Ittrom  tsdii  levandi  caofla,  qpod^o 

rebgs  .^(tiradis  naljpi  (olct  ^,  .otilittjtit^Cr.  coipmoa» 

flrandc  j;rttit  ddftrfntoi  fatnc  ad  fnater}am  Phiibfl* 

^Bodignilftmam  tpp1!cabot  '  Si)edentur  torpqra  ptj^ 

licnrria ,  toromqoe  Wrtrtthtriildi^  ektinincntor ;  '^^^ 

qaidem  corpora,  licet  non  finratltar' circa  Soieoi 'ln 

'Qrbitis«circ^laribof9  ^d  cUipiiciJB  ^ .j^taivsn  ejfondeflH 

'eAAtz  (!neeivoHt  pericolo  lainlf  ^^ffinit  pro  circola» 

f  ibos  ,  Soiem  habcmibDS  m  cerir^o  j  .  func  enim  pla* 

ilbctrtim  cllip(et  ptrlinf  dmnino  'b^l^^fricir ,  ac.prli 

indt  ^4  figoram  cireoltrem  protnne  a^tcdont ;   hinc 

tero  applieari  po(rui)t  corooribof  4(ti^i Jh  tUipfi  motif 

ti^,  'qut:  ie'  drcoio  dlArTimu     S^  ^primum  ^^  ot 

vidco )  doo  mihi  con(Utoet|da  Xunn  :,  upipm  p^i^* 

W»t  qUQ^  plineU^ijUtvis  Impendit  ^i^^porrench^ 

orbiam  rutm  ,  6t  ^rti^  ^us^if  rndius ,  qui  d^(^n» 

Pm  $  Sq\9  d(tfign«t,:  Uttr  inter^  ct)co|f  fiu^iii^ 

f «p  Uim?n  (I  probtri^ni  »K w  fubiAdc  jrdpcriaip » 

l^ffv^m^fQ  Mn  ntopabor,    .5it  igitur  Sp)  fp  ccntfO  fQjUh 

ih  ^Qndimmi  circt  botic  rcvotvttor  ia  cirtulo  om* 


t>imiii  in  mrcwh^  f ^ 


Vdnqs         •  >      -291  <•  fftooocoo 

Terrt  •  365  •  -§0000000 

Mars  •  ^87    „  «  44000OPO 

{opircr  ♦  4^1%  .  156900000    -• 

tMornas  •         10759  «  •taoooooo 

UrcogOQ(eancur Tirct  ccQtrs^^Si  quibm  ^irc  cocpioit 
fnimsntnr  Yerfus  $okm^  de^cgen^^  Cvflt  yelbcirttt^ 
ipfi>ruin,  qux  dcinc^ps  pd  fecundam,  drgniUt^ni  cie^ 
v«r«  dividi  dcbcnt  pcr  dill^Otiain  >  €|iiis  Wl  ceocralii 

^C  .  /.    : 

«   ^ .     Celcritai  inifCWCarj  6  IptpW  POrcjjrrupi 

■  .       ,      '.         ••  s 

ixvlietat  pct  tcmpiit  pcriodieum^  tisni  C  ^'  -i^-^  ^ 

T 
SpatiQin  vcro ,  qupd  d(carrit||r ,  clt  Qrbfti  cujafqu« 
]klanctc  ha^tepas  Ignou;  giiis  tsmen  qrbitiS|  (ive  pc« 

.ripheiiis.proportioniles  riint  rsdii,  qui  tunt  ip&  ^i* 
ifl:antiir>  dividantur  pidii  pcr  teqipPra  .revolutionuia 
Sngalis  planetis  propriarqm ,   qua'  in  ppcratipAe  r^to 

i  oegligi  pQ0qnt  trcs  nUiiili  didantigrt^m  ocnnicim  Zeri, 
«dbac  cnim  mancMt  mctiva  4i(^intiarQni  reiado  eadeip, 

£rtt Cclmciia Merciirii    ;^    itf    «cCC^  if^sf 

Vtoms     =.    97     n!«       ^    »4Qi 
Terrc       z:z      %%   ^       =    6754 

Jpvii    '   q5      jH    •       z::z.  la^ 

Oalt  eeleriiilt,  fle  eekrisitls  qfflsto  fecile  determi» 
nstar  vis,  qaa  finguli  Planetss  in  Solem  icndant,  «Mr 
vidcndo  qaadrata  celeritatnm  pcr  diii|flmtas,'five  ra« 
^ios  cirGaioram  a  Planetia  dcfcriptoram,  in  qnibus  <•« 
idtimi  Zcri  Iteram  (aivi^^^ttoHtf mi  mliHt.  ncgligi 

peiTwd      Obtin^ifw 

©Wf 


141    ^    sakn,  Ctptnrih 

-*''     GraririS Mercarii iii Sdlem  :=^'  fttct^to 

/Vcncris  *      -  '  =    fctc   41 S 

Tcrr«     •     -   '  =  projjc  »1* 

Mtrtis     "     •  ^        *      ?^ 

Jovis        •    .  ^'profic      H 

Sarornt     *   -  —  propc    -  a+| 

fffbm  rlrium  c^ntrtUam  rationem  fi))icire  examifimt 

rlmt9nut\  j9t  felSciter  comjfcrir,  maig^noque  Aflrono» 

foorum  boho  adnotavit  svircs  centralcs  daordtii  quo. 

rumvis  Pianetanim  crTe  in  ratione  rectprbca  dupltcatm 

diilanttarnni  #  Sole^  (cu  *:  vim  cemralem  imi  ejje  ad 

vim  eentriUem  %di^  ui  quadratum  diflahti^e  l£  a  Selk 

ai  gugdratum  iifiawia   imi  ab  eoiem  ^ie^       Resn« 

ita  le  hab^ai.  ^fcperiantor  t  Confcrantur  Planerx  duo. 

Terra^  &  jfupiier  \    erit  cx  hypothefi  %%^t  8  s^ 

MlV^  ?  ^^^  A^i  termini  rfti^nk  frima  defignanc 

gravitationca  TerreB  ,  &  yovuxn  Solcm :  ratiottif  Je^ 

cundig,  rekiprocgM  earundem  duplicatas  a  SoTc  diftan^ 

tiaSf  negle^Hs  6.   liltimis  2ens  diftanttai^um  flmpli- 

cium).    Si)^ewtoni  proportio  qbtineat,  erit  &dutn 

nie^iorum  ss  fa^o  cxtremorum;.  qu2  qnidem  faftt 

.licet  tton  omnino  irqualia  fint  (  oritur  enim  aot6oo» 

*  &  194688)  i  parufh  tamen  ab  'aiiquantate  abfiitit,  *ne« 

ittqnAm  9>(iit^ra ,  (i  in  calculir  foperioribiia  firaoio* 

Hfs  neg\e€tz  nw  fuiffent*  *  , 

,  C^rvtt.  IIL  ^  centreiif ,  99«*  -^rpm  iu  eoiem 
Hreuio  urgetur ;  c^j^ht  e/f^ '  ae  wvifVrmis  \  corpus  c-^ 
liim  in    circolo  l^^ilite^-mo^^r  ;   6c  irqDalibaa 

ra   •  ■  '   > 

CoreVAK  Sf  itptPJFtintuH  eodem  tempont  per^ 
eurr^ntur ,  eruftf  viret  iireSe  nt  radii ;  nam  com  mo« 
hili  lo  eirculo  mairsator  s^oabilicer  ,  erunc  celeriu* 

c  tes 


S,at  fyl^l^  «pdcfn  tcoiporc  decarA-,  4ii^^ut^pcrt<' 
zi\f  ^  <)\^«r   cun^  proportionalcs  fitit  radiif  ,  c^cfl^ 
^clcriccCfi  iU<lcm  rtdiis  proporciontUs  crftnc ;  h«  c. 

*,••',.*  cc[ 

C;i^'  1t»  '  Jioi  rcvociCi  SBq^tuofi^  pruicipc  Vzz  ---9 

llftii)w  RMKnifioffio  Anr  F  as  •-^«i^  sallfi 

Cdr^K  K*  S/  iivtrR  eireuli  esdem  *  eerieate  per* 
eurrafitiir  ^^  etmt  "virff^c^traies  iuveffr  ue  rMdii\ 
€»01  cnim  in  ctrekilis  omnibus  cclcricas  iic  conihos^ 

CC  1 

•  »«v  >«4««S  fcx.  tf      ^        V  ^V  • 

^  -  '4rMi,«^.  5?  iUfeffi  Vrd^H  lUiHrfii  teletiHiU 
h/s  percurr§nmr ,  ermt  vires  eetitraies  iti  ratione  cam'^ 
fQfisa  exdireda  radidNun  f  V  reeifreck  duplicata  tcm^ 

porttin.    Sco  cric  P^^  sc  «-*^~ «     Eit  ncmpc  in  oiftfii 

-     TT  • 

.r  .     ^**-  .      "  j  *  54 

motti  cqoibiUCdi  -^«^^  &^Ca  «--^;  hie  CC 

T  TT 

J»  --^t    <^<S8o^H~^,  &ai(ttAiUiikMio 
TT  R  ^ 

hibcbitur^as  —— si  — *^4 

TTH;     TT 

Gf-i^a.  Kri     jf /?  9  r^  enmt  vires  Hmrales  its 

fSH^  m*P^  JpHcm.fnttparttm  periMicpmtSh ; 
cum  cnim  fit  K  t  0  s  Rttit  TT^  iitidimii0  iv- 
sninos  riCionii  fccoulc  per  JK  Si^r,  bobtbitiir  V: 


I 

^ 


it&itamM,  enha  Utmbra  'ptfiodica  diretii^ut  Ihlj^^ 
Cum  tnim  tn  mOtu  cJr^uUri  ^  <|Ui  ^qbabftii^Cfl  ^  fpitt! 
tm ,  five  ptrjpheris»  atit^radii  finr  nt  tempoMi^  d(  ^y 
tiiSni ^fLii  K\r  iz    t\u  -        /  i.  r 

ptrcur/aatkr ,  ertuit  temptra  ptriediu  direSt  mt  taiii^ 
fgvtrjfe  *(  tilerittut  ;  iMtuin  omni  ilMttt  itqtMiiitt 
*•••*•  ..     ^    ■  .  .     ■ 

«ft  T,«— -i  liic  CMA  r.a  ^-*.»     . 

.     ■    ."  c  ,    •'■    c 

1 

t 

-    -         ^  Jl'    . 

— *   Seiii|><t  iitttiii  y  m  -^4  ^  &Aft  fii^ 

** .  >  •  ..  '  ^     ■  •— 

HintibMccit  >^ai  -^,  ii.».  Vi^m^fftlLtLtU 

Rtift 


IM.  XI.   «  r  SS  ♦,  «HM»  ^«1^4 

MCM  m  Mbtt-fMidi  cibntttttt  m  AimA  dirtadM,, 

•   ..       ••     .,■'■    ^.  .i'.    Jl  ■ 
■. '  •'  -•»'■  '       .CC .     .  .«4  i.  .       ,    ,, 


:v^^.     ..  \.  •• 


AM 


• ..  r'  AML^nr  IttfinitasHSAiv  fi  c>iiliii!<e»bQ»ari« 
iiOMbei-eMito.  Tfro  indiiftrtus  ftami^  ti^iM  opet* 
fictle  tilpBiiaetBr  veritattt  ftqoentet t  f .  Jlt  r.a  TC» 
Ijfi  bipc  U.  fi  C  tit  «,  «ri»|tt  r  st  T<  «,  di6  Jss^ 
UuB.ir  as  C<e;  fi^  st  r)e*ic  TC«  »;&  C;esai. 
'  '      Ki<        rr  "  CC 

♦  j  f.   W. '— «  — —  CC:  d  e,    hlitc  IV. ■  / 

TTr    tt  \  .R   , 

^  — i-  X  — i— ",-     V.  eum  -.^  *s  erit 

Tl*    .  ff  .      V.  ..«  TT 


WxvA  -—  .*  — .     Vf.  Si  r.a  »,  «|t  .TT .' 

"       TT       «»  ' 

/,  is  1?  t  r.  ^  T»  t  .^  i^Rt  /r.     VlU  }5i,lit/  Sl 
r  TT,  «ru  K  ss  v  i£c.  occ.     , 

."  §.  i8  j.  ttletrhMf  qua  mhiU  in  tirikh  rt» 
«dvHur^  tsjtm  ^l  fftm  tuttu  Mn^m^  ftct» 
k^filhfeyndtH^p&  OmUium  riumm  otaid^ 

'         .•  cc  ■■' 

f^0,,  pm,ln  ptttfti  circulo  F.sa-jr  (g. 

pfrce(L),ergoCC:£:  FR,tcC:::^  YVRy  qaJ* 
tcrp*^  uf^i.dc  raiionih|Uf^  4gl^»^r  ^t?P^  ^*^^ 
iic  ^iipli,  olitlncSituf  ..«iwn>:"C  ,s^ :  VT*  *VA  i 
h.e.Ctczz  r^FRt  r^vr.  i^mh*c 
cadftm eft celeficaa ^  quatp  corpus^^moteiitHi^ 
formiter  icceltnto  per  4aipidiam  radii,  par* 
tem  ^cquiferet ,  gtfod joflcnclq  t  Sciniper  Ja 
ftotd  uniFoVmitir  "iccelcfiio  S^    r'TT 

tur  -^  £3  l^rTJ  icmttm  A  a  a  rrr. 

i  .-f  ,      Por* 


Porr»  qai»  i|Mriuni.((l«to  iffwp<t»tqit»OBl. 
forratter  $tttAer»to  dccurfiim  eft  fiihduplMB 
illias ,  qnod  mobtic  eodem  rempore  pcrcorA 
reret ,  fi  M^tmHHtn'  movertfur  Telocitete  iHi 
iMeff-4 ,  quam  liabec  f^  ttmfut  ifiul-  (  $.  loA 
CinU.  /r. )  ;  8c  qau  celerit»  eft  rado  iaadi 

ad  tenpos,  erit  c  =:   ;    £ft  aRtem  it« 

T  - 

^VTT^  quod  paulo  fupramoniiij  proinde 

%WTT ' 
fa^ (bbftitutionefiorCs  — .    •  •  -■  ^  aFT* 

Wnc Tss  ,&rra—  5  qm^ 

ler  fi  ftibfticaetar  ih  c^aatiene  prlndbe 

/i  .     rcc      cc 

ts  rrr;  fict  —  j3  -2.  is  — ^j  undfc 

CCcs  — -  s3  «rjl.    Denfque  Ca  r 

y*  'S^*  i^t'  dtJcrittnJuhi  eireuJum  n«u  r»- 
^ltMtuTt  ut  iHt  etntripH*  fi^uatur  ratiMfm  i»» 
Virfim  Juplieatim  MJisntiartm ,  fiJ  fugieit  ^mc 
MM^M  Z>Jf  ffwitatij  ,  iM»</0  j»  i^M/»  ^  #^«ii. 

MM  4  iMire  dj^mtHf  |  CQrpBs  enimTn  peri> 

r  ^ 


i)0  mm  ifiilriuki  %$x 

pheri«  cfreali  moeutn  m  omnibtts  MhUm  fciji 

EuiYdls  «quaUtef  a  centrodiftat^  quAte  nU 
i)  ad  motucn  imereft»  utcunque  diterni  po^ 
HAtur  ieit  gravitatU  in  dtverfis  diitanti)!'^ 
tnoda  0c  fl^qualis  in  «qualibQs*  £x  eadem 
ratione^  quod  fdlictt  mfu$  in  cifiUy  mituk 
MH  aJiciMiur  uUa  grsvitatis  indquaHtatt  ^  confi« 

cies  ^  fuiiicere  quacncunque    graYjfatis  !#• 
gem<  '     ' 

|.  1 87.  Si  vis  gTMAstit  fiquatur  rgtkHtm 
inntrjm  du^lieMm  MfiMtitrum  «  ctmrt ,  truM 
etltrtutet  in  diverfit  cireulit  couttntritis  (  proin* 
dfr  &  in  «ilipjibus  parum  excentricis  )  In 
ratioai  rteiproes  Juplicata  di^tntitfumf  five  C* 
runt  inverfe  ut  radices  radiorunit    Andytitt  s 

t  t 

Si  r  a  — — ,  erit  C  «  — — «    i)#«f«  St^nifa 

t        t 

werit  T:  i>  a  rri  A/i  »  —  j  — ,  cti^ 

/1/5     rr 
CC     te         1       t 

fimiliter  —  t  — •  ss  — :  —  (  cam  Tss 

R       r        RR     rr 
€t  .     '    ^      CC  t 

<-^) }  proinde  ^-^  9  ■»—>.    Quantitatet 
H  R  Rt 

«(|ualei  per  eandem  qu«ntit«t«m  R  dividen* 

R        t  t 

doiobdnebU  CCa  '—  a  «— 1  Tam  Ca  — -• 


^f4  SiSi»IL  Gfm  VtL 

1 
§,  188«  rie^m  ;  Si  C  ss  »  mmr 

Vkru  iit  rMi$m  rtdfrtc»  Ju^iaas  di/tMtisrmm  % 

C* 
liam  ftnper  in  drcitlo  V  ss  — >- ;  cum  er- 

R 
I 
go  in  Fm£U  hypothefi  C  s  — —  •  confe- 

fR 

X  I 

qaemer  CC  ss  -t-i  erit  Tsa  «— »  fi» 
vires  erunt  inrerfe  ut  quadrata  difiantiarimi* 

s 

ScboU  KoCirtint  Aftronomi  :  Planetaram  ccleri* 
tfttec  efle  inverte  ut  radices  liiihntiironi ,  quidni  igi* 
eor  refte  intulerlnt  eorum  gravitttioncs  in  Soiem  efb 
ui  ratione  reciproca  duplkata  diHantiarum. 

$0  I  %$.   Si  gravitsf  fequmur  diHam  rsiio^ 
mm  I  trunt  quadtsts  tifffporum  foriodicQrum  ta 

1 
ttAi  difiantisrum.     Dem.  dato«  quod  T  ^  ^ — j 

RR 
X  R 

^  fict s2  (  iemper  cnim  !n  circulo 

RR        TT 
S  R 

V^  a  fjitfo.  Cbr./X).    Qua-i 

TT         TT 
rc  2*^  w  Ri  j  h,  #♦  Ti  :  I»  «  Ritn 

C^rotl 


Ik  nwHi  tfi  $trtuU%  %$f 

C&nlL  tn  ^€4dem  hypotbtfi  ttmp9f^  ptthdkajum 
mi  tMdicts  quadruta  trtplicatarum  di/iMtitiarum* ;  naia 
quia  TTt  tt  a  RRR;  t  rrr^  latnnque extrahendo 
fftdiccm  qaadracam  fict  Tx  t  22;  t^RRRx  t^rrt^ 

$.  190.   Si  futrint  tjuadrata  ttmporum  u$' 
^hi  difiaHliarum ,  erunt  vins  ctnttalis  in  ration^ 
rcci^rocA   duflicata   dijlantiarum  }   ^cum  cnin 

/      R 
V  ^  :— ^  (  §•  1^0.  CQroU.  IX.)  j    fi  fMdc 

R  1 

Rt  RR 

Siboh  L  QuoiiUm  Pltnecs  primftrii  dfCi  Solcffl^ 
4c  fecundarii  ctrcA  primarios  movemar  in  orbitis  pro« 
dcimc  circuJaribus ;  &  quia  quadrata  temporum»  pcrio» 
dicorum  (iint  ex  Kepfkri  inventis  ut  cubt  difianrta* 
rum )  binc  primo  Nemonut  collegit  C  tede  Boskovi» 
chio}^  urgeri  prtmartos  eum  {icundarUs  iii  Soleoi » 
iccundarios  in  primarios  viribm  decr^ceiitibm  in  ra» 
tione  retiproca  dufUcata  difiantiarUtJh 

Scb^l  IL  Sed  coi  ufui  tanta  ifta  tbeorematdAi  li» 
ries  l^  Dicam  :  maximoi  Singula  oumprimis  '^tti*. 
Hent  ad  motum  aftrorum »  tnatenam  ^bilofbpho  iant. 
digni(timini»  His  ^  atqiie  pr^cipUe  poftremis  altquot^ 
qii2  reguU  ada  Keppleri  audiunt»  iunitttur  omuis  tneo» 
ria  j^firoHomid  Seiptf)uianit.  Eoruudem  applicatio». 
tiem  vide  Parn  ll^  Sn&.  1.  C  1»  pag^  30.^  &  31%  Mi« 
tabor  I  (t  iine  Voluptate  legcCk 

Schol  tth  Maffarum  ratlonetn  babcndam  tf[a 

inmotiS)  dixialUsi  hictamcn,  ubi  tbeoria  prtfcni 

f  otiflime  rclf  lcit  tttotttm  iftrorutti  |  jtoorulto  caruu- 

1  t  Aemi 


$$6  SiOioIU  (UfiUJtlU 

dM  0011  HttxAni  proprcrtt^  quiHl  ¥ts  gnVtttfrit  fre* 
jK>rtionau  tiort  fir  iiMffii  anraaU ,  (ed  attrahensihM. 
Qnod  fi  fii«chijianim  opc  viret  eetltralcs  txpcrif  i  cotw 
tingct^  criam  mcCkroiii  ratio  habcnda  critf  &  oioiicii* 
cc  Gravefandh  (cqnentia  thcorcmata  locam  babcbunt  I 
I4  Sf  iuorum  corporitm  if  di/lauti^  a  cetisre  moHu^  %f 
titnpor4  fcriodica  aqUalia  Jmt  ^  vires  cjentraks  eruut  tit 
fnajfg,  11«  Sl  iempora  perrodica^  (f  majfr  tsqUitiei 
-fint^  vires  feqttintur  ratiouem  difidntiarum,  111.  Si 
fojitis  iifdem  tempQribus  feriodicu  tum  maffk ,  tum  di» 
fidntiee  a  Cemro  ifueqUaies  fint  ^  vires  eruut  tn  ratiofsi 
ox  iit  compofitA.  IV.  Si  in  eadem  Ijypoibefi  mdjfg  puM 
in  fatione  reciproca  iifiintiarum  ^  eruut  liires  ^qUaleit 
V.  Si  tum  majft  ^  tum  difiantiee  a  ceuiro  UtrinqUe  isU 
demfint  ^  Vires  ernnt  in  ratiofie  teciproca  dupiieata  tem* 
forlsm  periedicotum^  VL  Genetatim  ififtt  Ceniralei 
aruttt  in  ratione  compifita  ex  direSi  mdffarum^  ac  di* 
fiafitiatum  a  cemro  |  &  reciproca  dstplitata  tetuporUtti 
firiodicQrum^ 

Pe  mo(u  iii  aliis  Se^ionibus 

Conicis. 

§»  1^14  Si  mhile  Hpt&jeSiUf  t^  ctftttipi^ 
i4  ad  fccum  tendenti  ellippfn  defctiiit  ,  ejus  tii 
HHtriptta  variat  Vgriitd  dijlantii :  irefcit  in  mimte^ 
dterejcit  in  fnajorei  h«  e*  ubi  corpus  ab  apfide 
fuinnia  de/cendit  ad  imam,  cfefcit  gravilas  S 
ubi  ab  apfide  ima  afcehdir  ad  (hmmam  ,  de* 
crefcir*  Dimonjir,  Sit  area  JSn  ss  DSd 
(fig:<49.  );  Quia  tadius  ve<Sor  «qualibua 
temporibui  aeqaalcs  area*  verrit ,  &  viciflim 
C$«<790>  tifcelTc  cft  €odem  tefiipore  dc<' 


\ 


JD#  mitu  in  fiShnihus  09nmt.        %  ff 

(cribi  drcusil4^>  £cl>^;  hlnc  guo  tempore 
corpus  in  D  foU  vi  projc<^iri  impuiruin  rc* 
ceqcret  d  foco  ^  quantiratc  d  n  ^  Dp  ^  co^^' 
dcm  reniporc  in  4  foU  vi  projcftiK  anrma* 
tum  rcccdcrct  ^b  eodcm  toco  S  qiiantitato 
191  #  ;?:  4  f*  Ircrum :  quo  tcmpore  corpus 
In  D  urgenrc  (bla  vi  ccntrtpeta  ad  focum  S 
;icccdcrct  quantitate  D  $  »  codcm  temporc 
cc0ante  vi  projc<^iU  io  4  acccdcret  quanti* 
tate  4  ^.  Sunt  itaque  D  t^  U  4  €  fpatia  ^ 
qu9  mobile  fola  vi  ccntripcta  impulfum  de^ 
Kriberct  eodem  temporc,  Atqiii  D#,>  Ae^ 
quia  Dd  >  As  $  ergo.  Cumque  vires  (inc 
ut  fpatia  eedcm  tetnpore  confcdiia»  erit  l^is 
in  D|  h,  c»  in  diftantia  minore  major  ;  in  4^ 
ieu  in  diftantia  majorc  minor^ 

Schcl,  Bixi :  Df>  4  c  f    ^ia  t>4>  /i  ti 
finge  cnim  D  e  <  /1  c  ^  aut  =3    -A  c  ^   nunquam  dc* 
rcribetur  arcus  Dd^  maHcntt  fodem  iirc^iofic  vjs  prow 
jedihf  w  ufri^^fi  apfidc»    ,.. 

'  ■*  *.  - 

§•  1 92.  Jn  quAcunqut  St$iont  Conica  qus^ 
dratum  ctUritatis  tjl  ut  vis ,  ut  finus  anfftli ,  qu0 
direiiio  vis  incUnatur  ad  tangtnttm ,  if  ut  radiuf 
circuH  oJcuUioris  (dicitur  autem  hoc  loco  ciN 
culus  curvam  ofculari  ^  dum  per  tvh  ciua 
punAa  infinite  propinqua  tranfit )  •  Dtoit 
Sint  tria  cujusvis  curya^  pun<5ta  fibi  inBnitd 

propinqua  if,  E,H^  ( J^t  50*)*  P9^  qua^aga- 
tur  circuius  ofculator  H^A ,  cuftis  cenrrum 
in  C^,  &'cuius  perimetro  m  Q^  &  P  occiir- 

rant  reft»  <?  H^  £  R    Tum  per  duo  curvi? 

Z  3  •     illioi 


35S  StSidll.  C0futfIL 

illius  ponAt  A  ^  8c'E  docatar  reStM  AG% 
item  tx  b  agatur  C  /i  perpendicolaris  ad  EPp 
qox  ipGim  E  P  bifariam  fecabic  in  R  [  Pir 
Gtom. )  m  Denique  ex  eodem  cencro  C  au- 
catur  ad'  peripherijr  ponAum  E  reda  £  C 
His  pofitis  conrinuo  liqiiec  :  re&am  A  EG 
infinite  parum  diftare  a  pofitione  cangentis; 
fltque  acieo  re(Sam  CE  haberi  pofle  ot  per- 
pendicularenv  ad  if  £  G  (ptrGnm.y;  quare 
angulus  AEC  zz  REC  ^  ECR  ;  cumqM 
idem  A  E  C  :=:  A  ER  4*  RE  C  ^  fiec: 
AER  Hh  REC  zz  REC  ^  ECR\  mnn^ 
que  fubrrahendo  angujum  REC^  erit  AE  R 
s  ECR^  cujus  ultimi  finus  cum  fitf/l» 
0tiam  erit  prioris,  quem  elficit  dire^H  vif 
ium  ungenu.  Quodfi  jam  radius  fumacur  s 
2  9  &  unus  anguli  AER  r:  m ;  fique  reAa 
C£  drcatur  =:  R^  na(cetur  proportio  fe- 
quens  :  i;  iti  ss /{/i^tR^h.  e«ficut  Cff  adfA; 
quare  fAz:  mR^  ic  EP^  cui  atquiiralet  in- 
finite  vicina  G^sa  a  iii/l.  Porro  cdGH  k 
(7^=3  -£(?  «  ilGr  f  nam  fi  e  punfto  quo- 
piam  G  ducantur  du«  fecanres  G  J^i^^C  A^ 
crunr  fegmenta  GH ^  Sc  G  E  exrra  circulum 
pofira  inregris  fecanrifaus  reciproce  propor- 
tionalia  ;  proinde  habebirur  primum  prd- 
portio  G  H  :  E  G  z:^  A  G  t  G  J^^;  tum 
GH  X  G  ^-   EG  H  AG).     Igirur  pro 

GH  fiibftiruendo  valorem  ~— *—  (§,  iffo» 

C2 

CoroU.  VUL  ) ,  &  pro  G  ^fiibftiruendo  2  w  /J ; 

ircm 


D0  mtu  in  fiBiMibuf  €mUU^       ^ii 

item  pro  EG  pdnendo^,  &  pro  SO  ( ^a» 
dupla  e(l  ipGus  E  G)  ponendo  s  5  i  obciDt«( 

bitqr  H    2  m  JR  s:    5   M    2  5« 

Qiiantitates  «guales  utrinque  multiplicando 
per  C^  »  &  dividendo  per  2  St  ^  fiec  mRI^ 
P5   Ca.    Q,E.D.  ' 

ScM.  I.  Quia  f»  £  defignat  red«m  C  S ,  ^quft 
eft  dimidiam  chordx ,  gisam  circulus  o(cul«tW  e  di« 
reftione  vis  abGrindit ,  perinde  futric ,  fi  dicat :  ^a« 
dratum  vtl^citatis  effi  ut  vhn ,  ^  ebordam ,  qmm  cirm 
fulm  oftulator  ex  directiotit  vif  centripeut  ibfiindit  t 
ittnt  enim  dupla^  ut  fimpk.         -         . 

CC 
Scbol  U.  Qaia  CC  ^   V  m  R,  trit  V^  -— j 

mK 
len ,  v^  ttittrilif  trit  ut  quadratum  etltritatif  dirttfe^ 
f^  rtciproce  ut  dimidia  cborda  j  quam  eircuiut  ojiuiator 
mhfiindit  a  dirt&iont  vif  ipfiut,  Dimidis  chordx  (ub« 
{titui  poteft  integra  ,  cum  (  ubi  dt  rationibm  agitur  ^ 
fimpla  (int  ut  dupia,  >  v 

CoroU.  Theorema  hoc  admodum  elegans  eff  ^ 
fertiliilimumque  pulcherrimarum  veritatum ,  quaruoi 
•liquas  fiibjicio  t  Imo  s  Cum  in  curvis  onrynibus  C ::; 

(i>t7Q.CoroH.IK)  crit  CCsj  ^-^;   proind^ 

P  Pf 

^/* 

mRF::^ (4.i.  axiom.IK),  ^mRVPf 

PP 

AA 
r3  ^/^ ,  aot  K  =s   '  ■       —  •     n,  In(pc£ta  figura 


f6Q  SOkll  Qfmm 

S,  ^m  obtianv  btiie  proporttonefn  i  ve  rtd^  ^4 
uin  ingnU  CZ«  P»  itt  C  L  ad  CPs  fi^c  <  fi  ndiM 
yoiMtur;^  f,  fious  gngoU  Cl«  f  ss  n»,  diftantk  C£r 
9  Dp  porprndieolnm  CPs  P »  fict  s :  ms  DsPp 

P 
mgf^mD^P^Am e  ~.    Qqo rtlor» (obfttriuo ia 

D 

PRV 
Mnttlonc  CC^mR  F.crii  CCa  ~^|  &  CCO 

O 
CCD 
B^PRyi  mm  •**-«  s  K     Slmn idcm  rilor (hb» 

,.     PR 
ftiractHF  in  formal^  4 ^:si  mRVPP^  titt  AA  tsk 
rPPRV  . 

m. ^i  crgo  AADjBi   PPPRV,  fitf  a 

D 
AAD 

PPPR  ' 

4at9  quQvvi  umppr9  d^fcriput ,  ^  fimpliH  direSa 
difi^miic  0  ceitfrw  virium  ^  mm  rfcipr9C(^  mpliHU  ptr* 
fendicuU  9  cffi$r0  in  xmgmHm  demiffi ,  9  rr(i^m« 

fimplice  radii  cipcuH  ofcul^trif.     111«  M'm  0<culicit  . 
in  r^tionc  rcciproc«  triplicata  pcrpcndiculi  c  centro  iit 
ungcntcm  demiiQ  (ut  docclnr  in  $im€um  SiSimm 

I 
CfniMnim)^  (Irc  H  et  --^ ,  Vtlorclioo  i»  PoRtvm 

PPP    - 
.AADPPP 
formuU  fuWlituto  H^t  tV^  —   '^»;gsi^AD.  Cm 

PPP 

igirur  in  eadcm  <{a<ic«inquc  cqr?9  crc9  ^quaUbuB  tcm» 

.  poribqs  rlelcript«  fcmpcp  finr  flpquelcii  C  JT.  179, )  9 

omif^o  fcrrnino  co'iftuini  ^A^  Iwhcbltur  T  s»  O, 

b,  c  vif  rejpitim  cmmm  c.  c.  itlipfiQi  ffi  dirf&f  »1 

dijiftfh 


4l/kntin^  a  mtr^^  Snp^C^op  plaribus  recitdndls, 
gusp  qai  vol^t,  BQshvhbinm  a4c»t  m  Sufpktn,  a4 
fb'dof^$tayamm\  fcd  Mathefim  pi;obe  callcac,  opor* 

'  §.  193«  5S^  Jffiribatur  fU4vis  StHt^  Qanics^ 
virtum  ctntro  cxijhnu  in  foc9 ,  crit  vis  cmrdis  if$ 
rsiiom   rcciprocg  duplicsts   JifiMtiarum  j    Cc^X 

V  9:  —  •     Tkm.  In  cllipfi,  &bvp<jrboU 

perpendiculum  o  jm  in  ringineem  demiA 
fum  e(l  ad  {emiaKcm  cransverfum  ,  fKut 
pun<%i  conraAus  dtftantid  a  foco  eft  ftd  per« 
pendiculum  §  cmroxn  cangentem  demllTuiii 
(  fcr  cUm  Sc{f.  Omi.  ) ;  quare  fi  perpendicu*» 
]um  e  foco  in  tangentem  demtfium  dicaeur 
w  P,  femiaxfs  transverfus  ss  i  (  eft  enim 
^ntitas  conftans )  ,  diilantia  pundi  conta* 

D 
#uFafoco  ss  JO,  fiet?;i=3  Dj  "^j  bie, 

P 
perpendiculum  #  mtro    in  tangentem  de^ 

X> 

mifibm  ss  — -t    Cum  vero  radius  circuli 

P 

ot&ttlaroris  fit  in  ratione  reciproca  triplicatA 

hu}as  perpendiculi ,  erit  R  ^  ^'^  \   q«<> 

Talore  (ia  formuU  V  53*^  )  pro  R  /bb. 

Z  5  .      Ww* 


c 


r. 


A^  DPi  A*  • 

fiicuro  fiet  :  F  z^  — —  —  -* — .     be» 

D%  P^  D»     ^ 
ram  omiflb  termmo  coaftanci  A*  ,  obciiiebi* 

I 

torr;:s  .    Q.E.D. 

DD 

CoraU,   Etijoi  in  panboh  (  in  qnam  dlipGsy  ^ 
fiypeiiiok  abcaor  ^  obi  axis  cvadit  infinims  )  cft  K  =3 
I)DD  I 

■  ■>  ■  ;  unare  cdam  tn  parabola  J^  ss  — •  Dieam 
PPP  DD 

iaoicn  panlo  infcriof  :  ad  ddcribcndain  parabolam 
omnino  rcqoiri  ,  ut  ria  ccntralit  eanicm  dirtSiwcm  ^ 
&  maguitudhtitn  confiantem  lcnrct. 

%.  194«  Cireuhu  tftuUur  JkJUndit  s  din» 
flicm  vit  ctntriptu  quadruplum  $jus  skitudink% 
fer  qitim  eadvrt  dtbtt  corpus  grmritau  canfiant$ 
( ijusm  babtt  in  cs  difiantis  )  ut  se^mrat  tsm  tt^ 
hritatem »  qua  projicitndum  tft  ficundim  datam 
dirtSiionimf  ut  dtfiribat  datam  StBiamm  Com^ 
cam ;  b.  e.  chorda  circuli  ofcqlantis  SeAio«i 
nem  Conicam ,  &  trait/icnt  fotum ,  in  qua  tft 
ctntrum  virium  agtntium  in  ratione  rtdproes  du^ 
plicata  difiantiarum  ,  eft  quadrupia  d\&x  alti» 
tudinis.  Dem.  o(culetur  circulus  SeAionem 
Conicam  \n  E  ify  prae»  )  .  Sit  cenrrum 
virium  alicubi  in  ^  per  quod  tranfeat  chor- 
da  B  P.  Sic  denique  dire^io  projeAionis 
E  G.  Pono  mobile  in  E  habere  celeritacem» 
quam  acqiiireret  cadendo  per  £  /«    In  da-* 

ta 


I 

Di  motu  in  fiSlfomhus  CQfiMs^         3^3 

ta  hyporhcfi  corpns  eodem  remporc,  qno 
motum  uni^ormiter  accelerando  decurrit  E  f^ 
motu  acquabili  conficeret  2  E  i  (§•  160,  Cot\ 
Il^.  )•  Irerum  eodem  aliquo  tcmpore»  quo 
corpus  motu  uniformiter  acceicrato  defcriblt 
GH  :=:  E  P^  di<aa  cclcritare  projedum  de^ 
currit  EG  ;  proinde  Ei  ^  Sc  GH  defignant 
fpatia  motu  accelerato  confe£i;a  ;  tum  Tcro 
^  Ei,  Sc  E  G  fpatia  eadem  celeritate  a:qua^ 
biliter  dcfcripta.  Si  autcm  C  =:  ^,  habctur 
S:  /  :=:  T :  ^ ;  quarc  lincis  2  Ei  ^  Sc  E  G 
exhiberi  pofiuht  tcmpora.  Jam  confcran^ 
tur  fpatia  £  1  ,  8c  G  H ,  mocu  uniformiter 
accelerato  defcripta  ,  quas  fiint  uc  quadrata 
temporum ;  erit  propterca  Ei;  G  H  zz^ 
Ei*  :  E  G^  ^  Multiplicentur  tcrmini  ratio- 
nis  primac  perG^;  ficit  £i  h  G  Qj  GH 
X  Gj^z::^ Ei^  :  EG^  .  Ettvtro  EG^ 
r::  GH  m  Gr^  (  fi  enim  ex  eodem  pundo 
G  ducacur  altera  (ecans »  altera  tangens ,  cft 
pir  Giom.  tangcns  mcdia  proportionalis  inter 
totam  fecantem  G  Jpf  &  ejus  fegmencum 
GH)jergo  fimiliter  4£i>  ss  Ei  M  G^; 
hinc  fa<^a  apqualia  in  proportioncm  folven- 
do,  obtincbitur  :  G  J^J  %  Ei  ^^  2  Ei  t  Ei^ 
Quonram  autem  6  ^infinite  vicina  ponitur 
xtAx  EP  ,  &  arcus  £ /f  infinitefimus :  fumi 
potcft  G  bsi,  E  P;  qubrum  altcrum  alteri 
fubftitucndo  fict  E  P:  zEi  ^  2Ei  :   E  U 

Igitur  EP  M  Ei  :=:  4£i«  ;  &  £P  s:  — 

Ei 

^  4Si.    Q.E.D.  .       Sfboh 


5^4  S^^hJh  CaputVIl 

Scbol,l  %\Ei  «   GO^G  H  ¥i  QD  =!    4- 
Si^  ;  £G^  ;  fict  alternando  .   £;    «  G^r^  Ef^ 
Si    C//'k    QQ:  EG^    ^proindc6£G»     =;  GH 
K    O^,  itidcm  erit  4  5/^    =:    £i    x    G^  J    Wim 
prpporno  i^ft  rationum  irquftlitas, 

.    Scbel,  II,  Qud!  hticnfque  dipci ,  illuftrabuntnr  («' 
q^enti  probietnare  ;  Dat^  quavis  curv^ ,  ^  ceiifro  vh 
tium  i^  in  qMouif  cHrya  pun^o  4tterminare  vim  eetnri^^ 
fetam  ,  ^   celeritarevi  proje^ioniifr         Solntio  %  Daro 
(]qovi$  arau  cu}iisvis  curvs  datur  ope  Geomi  cireulijs, 
qui  Gurvaii)  in  dato  pun£)to  ofcuierur.     D^toquQ  ceni' 
tro  v(rtofn  datuF  chorda  circulo  oftulatore  intercepta, 
(cu  chords^  ft  dato  purvae  pun^o  per  focum  trmfiem^ 
(k  $d  aiterum  circuUris  peripheriat  pun^^um  tennind» 
19 ;  b«c  duc^tur  primum  \  poftw  ccjcrira$  corporis  in 

CQ 
quncttnqj  curva  rcvolut^  invenienda  cft  (  nam  F;a  — — 

mK 
^.  19»«  Sehol,  ILJ »  Invenitur  autem  ope  perpcndi* 
culi  in  tangentcm  duQi  (§•  I79*)i  quod  data  corva 
tibiquc  datUP.  Iftud  ad  vim  centripetam^  ^d  eeleri» 
fdum  projfQionis  quod  facit,  dabit  eam  (  p9r  (tnte  di» 
&$  )  quarta  para  cbord»  ^c,.  Arquc  bsc  gencralis  cft 
iblu?iO  ad  omncs  curvas  pertipgens»  fiiirum  fim 
(  {cPibit;  Noftcr  ) ,  quqnfi  ufus  fint  pieorem^ta  bae  ge* 
fier^fia^  qti((  ftd  cajus  particularet  appUcatt^  plurima 
filia  pr<(hent  5?  elegantijjtm^  i  ^  fitiiijjima,  Sic  quo* 
niam^  Uffi  motus  pt  in  circulo  cum  vi  4ire£f»  ad  cen^^ 
frum^  (^Hgidm  vis  cum  t^mgcufe  tvadip  re^tis  ^  i^xbern 
4a  ,  quam  circuhs  ofiulator  (fbfiindit  q  dire^ione  vis^  efl 
ipjtHS  eircuh  diat/feter  (  cuin  per  cjus  centrum  tranfirc 
j^eb^at,  6^  quivis  circulus  ul>ique  fui  ipiivis  ofcitlaror 
fif  )  \  facih  ex  tl>*oretnatii  espofiris  derivantur  ea  om^ 

Vfiii ,  ^n^  circti  virfs  mott$um  circularium  prodidif  Hu' 
^fnm ,  c«m|>ricn{s  ^V*  i^rohgi»  ruo  ojcillatorio, 

Sciol. 


— K-n 


1>$  mdtu  infiMi^nihus  toniciu       %6t^ 

ScbcL  tlL  Ad  peculiafcs  {blutiones  qu6d  «ftilief:^ 
clttilbeiitur  es  d  pectiiiaribus  curv«rum  naturis.     Si^ 
in  ellipfi  jacet  pundluAi  i  inter  S  ^  &  £  /    sn  paraboU 
eongruit  i  cuitl  S )  in  byptrbota  jacet  S  intcr  i  ^  6i  E 
(  f f^  Ge0i7/.  )  4       Sequifuf :  Si  ptojeBionu  ctUrim 
iAnta  fit  {  qUamam  carpvs  i  tbto  projidionis  ad  ctntruM 
\iirium  tadend^  adqttirerit  manenu  fadim  Vi  eentripM^ 
dejhribindam  ejfi  parabaUm*     Si  ea  celetitai  minor  fit^ 
allipfitfH    Si  deuiqUi  majdr  :  byperbolam^       Sed   ritn 
Univirfi  Catctilo  difiniri  apirofiw  eft  ,    quain  ut  ferri 
tytdnei  pojfint  t  tccito  noitruiti  Makd*      £t  Boskovi^ 
cifitts  i  non  vacat ,  (cribit  |  in  buJM  generalis  folutionif 
idnfideratioui  immorari  diutitis  ,  ix  qua  ad  particutant 
iajiu  mtilt<t  operoftor  efi  difceiifns.       £go  Veritati  baie 
dariffimc  5  quiH  Tyronibtts  propolieiidie  tntiltutti  itt->^ 
hsii  I  hodiequc  inhitreo  i   fortc  •  •  <  <    Safficiat  lii« 
tefea  cogtiltio  hiftmrica ,  cajbi  reiiiit)i(centifl  ad  motum 
afltdtum  apprlfnc  ncceftiria  eft^     Pbilofofbtca  ^  fed 
Tyfotiibus  peroblearc  habetur  in  Dijferti  Boskov.  da  ' 
ihotu  corp»  aitri  in  Citttf*  immob*  j  itcm  in  Btcyi  tbictis 
Scbifffl  di  motu  prajiSi 

§i  195«  Dum  taffut  eUipfim  dimtiHi  Jb 
dpfiii  funma  defcandit ,  motuf  ejus  iJentidem  ae^ 
(teletaiur  x  dumque  ab  ima  afeendit ,  femper  reiar^ 

datur^  Nim  Ctmpet  iti  ellipn  perpendicula 
in  tangentes  demifTa  decfe/cont  pro  rdtiona 
imminutarum  diitantUfom  a  foco },  proinde 
cam  C t  #  cs  pt  P  {§i  179*) ,  m  dercenfu 
\  per  orbitam  ellipticim  mocum  accelerafi  ne«^ 
N  cefTe  eft«  Contrarium  obtinet  in  afcenfti  } 
trgOi 

CotoH*  1.  Proitldc  in  carpotif  Jifaft/U  pit  illipfitti 
i)ii  ptojiBilU ,  £^  cantrifita  ccnfpirati  dihit  fub  angu» 
to  aittto  (  $.  11%  )  i  iu  afanfu  fub  mtsul&  abtufb 
(iiid.HlI}^      -  .        Cmtt. 


$6S  Sc^iff  11  Oput  m 

Cor$U^  IL  Kurruni  c^rfus  in  tUipfi  difiendtnt 
mtttdit  md  ceutrum  vitiUM  f^^l^jC,  }  i  iuiifcenju  rtcf 
dii  ( ikd.  Kll  )  . 

SihoL  I.    His  omnlbus  ex  amaditn  cognitis  fa^ 
cllem  hab«nt  explicatum  pba^nomem  fequuitMi  ^    ^* 
l^Uiieta  cirta  Sokm  (  aiu  centrum  aliquod  noix  long# 
diltans  a  fliperficie  So\\s  "^tnovtmur  iu  orbilfus  prpxi^ 
me  ellipticis.     Ratio  cft  :  quod  vi  primum  cewtri  eti^ 
ferantur  in  Solcm  (  aut  ccntrum  aliquod  Solis  {iiper* 
ficiei  vicinQm  )  ,  pro  ratione  reciproca  dupiicara  dU 
ftandarum.     Tum  quod  mox  a  fai  creatione  projeQi 
fuerint  minore  velocitate  ,  quam  fit  ea,  quam  Pitne^ 
tc  acquifiviiTent   e  loco  proje£lionis  cadendo  ttlqu9 
•d  ccntrum  virium  manente  eadem  vi  centrjpeta  (  {m 
%^^.  ScboL  IIL) .      Alii  dicunt  t  quia  minori  c^leri* 
tate  projedi  fuerint ,  quam  quae  mobili  in  orbita  cir* 
cuiari  retinendo  fufficiaf.     Dicunt  idem.      IL    Pla* 
neta  moventur  iu  orbitis  varit  excentricis  {  dicam  vero 
Fartt  II,  jf.9.  excentricitatem  eflediftantiam  centri  el* 
lipfeos  a  foco  ) .  ^.  in  caufla  eft,  quod  varia  etk* 
titatt  projiciantur ,  quantumvis  (emper  minore,  quani 
quc  de(cribendo  circulo  fufiiciat ;  itcm  quod  fub  va* 
ria  dirtBione  vis  alterius  ad  alteram.     Quo  celeritae 
projedionit  major  eft)  aut  quo  minns  anguias  acu« 
tU8  abludit  a  Tc6ko  y  hoc  magis  orbita  elliptica  acce» 
dit  ad  eircularem.     Qus  autem  orbit^  magis  ad  cir» 
cuiarem  accedunt  ,  earundem  tnajer  effe  debet  axit 
tonjugattu ,   ac  propterea  miuor  exceutricrtns.    Nam 
cum  in  omni  ellipfi  qudfcvis  dns  re^ar  cx  focis  ad 
idem   aliquod  perimetri   pundam    da£kx   adirqoent 
•xem  majorem  C  1^^  ^fi  proprittat  tUipfeas  )  debet 
]>rofe£lo  majori  axi  conjugato  refpondere  minor  ex* 
centricitas  i   minori  major  ;   ut   con(ideranti   patet. 
IIL  Plaitetet  tmvtntttr  in  arbitii  varie  Bd  EclyptkMm  in» 
aiinatif»    Ijt.  ctiam  iftud  repetendum  eft  a  varia  com» 
UnaMnc  vii  jrojcitiUs  cam  ceacrif  cta»    IV».  PUutta 

dtfcri^ 


Le  HMu  infiiHcnitus  cowdu         $67 

ieferilmnt  €re/is  temporilus  profortionnUf,  ^«  dcfcri* 
bere  debent;  nam  iftud  in  quavis  cuiva  fieh  dt;b«fi:e^ 
doeui  ^*  I79t  CoroU.L 

SchohlU   Jam  qn^fita  aliqtiot  expcdlam,  qnae 
11(111  erunt  inmotu  iiftrorum^      Q.  L  Cur  Flamta  in 
eUipJt  cirea  SoUm  revoluti ,  confeHa  periodo  Ji/a  y  lion 
fofdent  inter  fixm  Inerere  videntur  ?     Notflrunr  enitn 
Aftronomi  :  poft  piurium  annorum  decurfus  altidi* 
jnum  orbit«  planetarix  puntlum  (  apheUum  vocant ) 
non  easdem  inter  ifixaa  ha^rere  »  quas  inter  hsrebac 
alias.       VjL^  tribuendum  iflud  accidentarta  caulTx ;  fci^ 
licet  2  mutua  Pianetarum  omnium  attradlio  eorundem 
tnotus  leniibiliter  perturbat ;  hinc  apheliorum  progreC 
lio.      Q.  II*  QuomOdo  penes  Flanetas  qmdrata  tempo*^ 
Tum  periodicorum  fentper  fnnt   nt   cubi  diftantiarumi 
i^.  ad  rigorem  loquendo  :  func  ut  cubi  diftatitiarum 
duntaxat  mediarum  y  in   quibus  aifefiiohet  ellipfcot 
conveniunt  cum  afFefiionibus  circuli ,  qui  defcribere* 
tur  media  illa  diftantia  pro  radio  aflumpta.     Quoniam 
vero    orbitac  planetaric   admodum  parum  excentricet 
funt  (  nam  ,  KeilJio  tefte  ,  excentricitat  t.  c.  orbitc 
Telluris  compleclitur  fere  17.  earum  partium  y  qua.* 
rnm  icoo.  compleftitur  diftantia  media)  ,  fumi  po« 
teft  :  easdem  eflfe  afFediones  orbitarum  plaiietariarumy 
qu9  funt  circularium ,  ac  proinde  pojita  lege  attra^to» 
nis  agentff  in  ratione  reciproca  duplicata  diftantiarum 
cfle  quadrata  temporum  periodicorum  ,  ut  cubos  di» 
Itantiarum,        Q*  IIL    Cur  Planeta  ad  diftantias  na* 
dias  delatiy  in  quibus  cffdem^funt  afTc^^iones  ellipfeof^ 
qu£  circuli ,  »0»    circnlos   defcribunt.      I^.    quia  vit 
tangentialis  cum  centripeta  non  confpirat  fub  augulo 
redo ,  quod  tamen  circulo  conficiendo  neceftarium  ef^ 
fc  docui^.  i^V     Statucndum  itaque  :  nonomnes  ^  £ed 
plerasque  ellip(ium  afFefiioncs  in  diftantiis  medii/  eas* 
dem  efle ,  qux  funt  circuloium.         Q.  IV.  Si  confpi' 
ra$io  virium  Jiib  angulo  nBo  faciat  ad  defcriptionem 

€irm 


X 


%6i        mttuc^ptt 

etciiU  ,  fuU  ifl  ,  quc^-^eaMita  (  hAtt^t  fttteeiH  t« 
ilti(TititO|  &  itifimo  (i/mitst  elKdeieiS  panao  ^  h«e«  in 
ipfidibu»  ^  Hon  defcribtitMr  circuh^  1     1^4  quU  ddlcit 
Velocitai  pfbje^tidnts  reqdifiti  id  (Hrculumi        Q.  V^ 
5/  prb  iiAtia  qUaiUiiaie   iiii  mttipH^^f    ittrHque  pr4 
iiaria  CektitAti  prdjc^ionu  ifHitia  ift  6thitatum  cutveth 
C§*  l7$'Jl  qiiom$d&  in   Utfaqui   apfiii  ^  ttbi  dii/itfd 
/jalfitUt  tS  vif  UHtripiia^  £/  pt&fiQUif  ,  iatUw  ift  or» 
hita  inftixio  }     tji.  quii  nttn  trtOdi  a  ^ttiititdti  %iifcett^ 
ttipita ,  &*  ptojfdiotiit ,  (cd  veto  itiiin  ab  attgttkfttni 
vatietati  pefldet  cojusvii  CutVc  iftfiexio  (  ibid,  )j  qod* 
rum  ono  defieieote  compcnCitio  fieH  poteft  per  ilittd« 
Q.  Vl.  Si  PloHata  in  iliipfi  tevohitut  utgeatut   Vl   ceit» 
ttipita  agittti  prO  tat^  invi  dtipiiC,    difl.\  qUi  fit  ,  Ut 
iiOH  fuiindi  iu  CHtttitm  fuUtn  detabatur  «  Ci  C«  Luttd 
in  iirtam  «  rW/01//  flanetd  ptipiatii  in  Solitit ,  ficUn* 
darii  in  ftios  prtmattos  ?      Sane  tuin  'i>U  Cinttipita  in 
attiffinio  otbitti  tUiptictt  pUitSo  taiitte  fit  tjficacitatii  ,  Hf 
flanetam  adcideti  cigai  ad  focum  ^  fieti  iiiutiquam  /v^ 
titit ,  Ut  in  imo  femita  fuee  punBo  tecedat  a  foCOy  uii 
pto  qiiadtatd  immiitttta  diflantiei  Mim  ciHitipitom  auge* 
fi  UiCtJfi  ift.     Qttatifa&a  contittiniet  acceJftQm  ad  fb^ 
mm  delit  fiikindi  in  foCitm  delabi  ^  mqui  iUipfihi  iti* 
figtam  difcribiti  pMfl^       MxC  eft  rotetutis  illi  obie« 
ftitio  eosufti  otntiiom  ^  qoi  t^avtotti  pleCitis  idm« 
fintdr«       t^*  <{t|  iioti  ibfiOd^  eft  itt  iiifimo  retHit* 
illiptictf  ptmdo  matcima  vis  tntttipeta  >  it  fimutfM» 
feima  efl  Ptamt^  vetocitat ,  ic  proinde  iterttm  ntaxi' 
fha  aii  cmpofita  i5c  anttall  ^  t^  tangiutiaii ;  Ctfjoi  di* 
tidio  tititum  «t)ert  1  ot  id  eetitrom  viriom  retidit  ^ 
fie  potioi  Plitietim  ab  eodem  iVerrit^      Sed  hititf » 
bojorctoe  iimilei  objeAioties  allii  ad  ntotum  afttotunt 
ibuttdi  I  &  ipiii  Bosliovitbii  Vcrbis  dilttam*    InttHf 
IWtf  f  rtiibidi  ftifiiciiti 

Pa- 


De  m6'tii  gravium  terteftrton» 

%i  X^ti    Girdvii  4Uifi»  pi^yiSd  (k^^ 

ke  I  IC  gi^ayiticis  difedione  id^crikmt  ^0^^ 
toUm^  tujus  Ufigtns  tfi  iffs  fti^i^fris  ditettt^ 
A  B  (  /%«  5 1.) ;     DcMi    Si  graVe  proiicUtttf 
fectlndiim  il  B I  8c  inret-ei  ti  gravitAtis  ilf-i* 

fearuf  feeundam  if  R  ^  ufgebituf  gemiah 
iribiis  diterCe  rationis  ^  qaarMna  altera  mi«.. 
.^riMfi  eil  ^  mufkrdHr  alcera  ^  qiiare  ibolHle 
Tpia  unifarmi  projedrooe  impiikimi  fioj^uliir 
rguilibuf  cempufculii  derertberet  fpatia  ik 
qualiiifCi  Ci&{  ^fel*  incem  gmvitate  fpatit 
In  ferie  numerorum  impartum )  hinc  utris* 
que  viribbriiflimiifdmene  debec  primo  Mm* 

J>u(lulo  in  f|  altero  in  K$  q^*  punda  noa 
acenc  in  eadem  tt&^  ($4  ^g.)  t  fed  in  cuia 
Va  p4rJb^U€Mk  Nam  in  mocu  aniformittr  §1(1^ 
ceterato  fpatia  funt  ut  qUadraca  tempoi*tfm  \ 
tempora  aucem  deiignantut  Bneis  AC^  A  O- 
(  cUm  in  motU  arquabili  fp^cia  fiht  Ut  tem» 

pora)^  fiett  AEt  Afs  AG^  i  A  Hi  ai 
£ti  i  1X9  4  Siirit  vero  AS^  kAi  ibt^lC^ 
Ik  :  £t^  tcPK  femiotdinicje ^  proita^e  qui^ 
Am%  (emiordinacarum  ftlnc  Ib  Utione  ab^ 
ciflrarum «  qu«  eft  prdprietas  patabolii  lli^ 
behiis  AR  pr#  diamttro  i  «rgOA 


^  I 


I^     ^  iWKii/t  Cf«i  m*  a 


^^ 


SeM.  L  Similiur  ^  pxtf  oppofiit  de(crftetiif 
firtbolt  y  fi  eorpiis  6bli<|afc^As^cMlar  iecnncloiii  du 
ffodionem/f^.  Nec  modo  fi  oUi^^  (ed  eciam,  li 
itmi^h.  futSt  direffio  {viijeaiohti  ( J%.  5  s*  /  P^ 
ffftboiam  defoibi  neceiTe  eft.  Coniicitor-  iftud  proDfl« 
Ctone  etdem  i  qoft  paulo  mox  u(i  {bmus.  Immo:  fi 
CVpps  noi^  qoiJem  projici.i  (cd  alit  vi  (econdtim  ro« 
ttamhorizonttlem  «briplpohanias,  itt  tamen,  oriis* 
teiet  etitm  ri  {rtvktcit  delcendar ,  iterum  paraBoU 
dt(ciibetor.«»  hOtrvaUo  uon  admodum  magHo  j  ^o<ro 
cpin  ixigtm^  fkUqmf  sircuH  ttrrefiru  arcm  f^ro  re&m 
hark&ontiii  adfp^um  baVeri  podic ,  grave.qobdvis  'ff 
h^  U0i  iuntis  alto  de(bcndens  ptrabolai^  4^(^  ibit  in 
liypotbcfi  tcrrae  motj^.  Sed  tnim  :  dtSum  faraboli* 
^ik  iiou  ohfervamu$.  Quid  ita  non  ?  Jfj^.  in  cauAt 
€ft*/<]|hod  tint  cum  terrt  hOrizpntititer  moVeamar 
siiicli  c^inmotai..  Sic  neqoe  (i  qois  ntvi  celerrter  pro* 
pulfii  ytdot  moio  eoMmoni  movettor  ,  tdvertit  Itpi» 
cltffi  jCi  (iumnitttO'mt&  demifloa.  cutvtffi  dtilribortl 
wiv^fUi  w^ini  ^ptOttor:  in  litmt  conftitonu^ 

SchL  IL  Hxc  corponioi  joUiquf »  tot  boritoa>» 

uttter  projcQorum  theorit  noh  obtinct^  ubi  five  t^riir 

tiJiflinHa  tAotom  imptdit «  (ive  graviiaiif  magnitudo  ^ 

tot  direSio  non  eadeiii  pcr(ever&t«    Ncmpe  s  ctirva , 

4jfuxn  proj^£lilt  de(cvfttt  In  tere ,  plurimnm  recodh  d 

furaiola ,  if.acotdh  adfirmam  byferboU  ,  ftmro  ad 

tfflihn  quandam  Mjjfmptotioam  acctdtnte  iu  infiuitumi 

i^  ufptom  congfttuttii  \  quod  quidem  accidit  fotiffimum 

in  globis  minuf  potulorautibm  |  vel  ubi  cum  ingenti  ve* 

locitate ,  y  feupbili  eUvatione  fit  pr^eSio. ,  ut  gUbut 

4d  ingmem  difianiiam  abeat ,  ^  refiflentia  dtu  agat  / 

iUmt  repflentia  de  motu  ficundum  direQionenr  projeBio* 

nit  uecepto  ptrpetuo  aliquid  detrabit.     Itt  Boskovichim* 

Etdtm  illt  terii  reiiftencit  cfficit  ,  ne  fiuida  c  vtiii 

crumpentia  ,  tu^  tatut  ex  tngoats  ctntliboi  direAio* 

ntiid  borizoncem  mdijutt  profiUences »  corvis  ttome 

ptrt- 


B$  mfu  gmvium  urrifirikm         fft 

))ariDoIicfl$  acfcnbaiit;  lea  diu| r||X|f  ad  pflraboum  if» 
otdctuci^  -9^*^?  rffAvitautn^  yero  £^  AOQ^  ^^ 
qiicnrU  :  cum  grdvitat  tonvergat^ti^  Terra  cmtrum^ 
^  dfcrjrfeat  m  r^iqti^  recipr.'  d^tic.  4ilh»^4^f4i(H, 
dibct  dcJtrHi  arcus  hypifrhola  ^,  a^l .  cUi^m  JuUitipt^  /i^ 
cum  in  coffro  Terra  fto  var^^^^^kcipqte  prjif^$,fi[^ 
jeiiioHUf  ^u^.tatnen^in  nofiris  frtpJeQi^itu^t-^ffM^ttf^ 

ferimur  in  fuper^Cfe  TcrrKf^  PvP.^^^^  ¥^  <t^iK*'^t  f9 
fUipJirn  inducat  ^  qt^dt  tanten  oh  impiOHem  d^autiam  iU 
terius  foci  a  vertke  froxinto  atteri  foco  ad  pmrahoUu^ 
^cceJit  quam  proxime  ,  ift  fuam  iUigfis  iu  mm^tifum 
ilblongata  defiuit  tandem^ 

,  ScboU  III.  Si  arcui  jil,K  G  (Q>tcndAtur  ciiordf 
i^G ,  dciignabir  qa  difiamiam'^  xcda  cniniyriiQflr  con» 
ifiedit  obje£lam  fi^rieos  tum  fericndO|  dicitnr  dtfimf 
tiafirnpticiter*  Qliod  fi  ab  objcclo  ^u.fericQte,  (n 
fcricndo  dcmittatur  pcrpcndiculujn  ad  borixontcoi  ^ 
iflud  dicctur  ahimJo  jaaut,  Ricda.autcm  RO  iuMfp 
perpcndicuium,  &  fcricntia  ,  aut  feriendi  locnffi  in» 
(ercepra  ,  audit  iorizontatu  difiautia ,  qoc  etiam  a$n» 
ptitudo  ja&ut  in  horizontali  dire£kioQe  yojKa^i  (bUr^ 
Porro  expcricntia  certum  habemui  :  maximam  aro* 
plitudinem  jaQus  obtincri  fub  .diredionc  45^,  fluc 
paullo  miiiore«  Dirediones  ali«  atqualiter  a  45^  dif 
ftanrcs  (  c.  c.  fub  angulis  60^  i  &)<><' ,  aut  70^ »  A 
so*  &c. }  ad  eandcm  ja^lus  amplitudinem  grave  dc* 
ferunt  mancnte  eadem  vi  imprefla ,  h.  Ct  mcniui^ 
pulveris  pyrii ,  mancntibus  eodcm  formento ,  codca4 
^uc  globi  pondcrc  i  hinc  eft ,  quod  idcm  ja<^8  dof 
plici  dire^lionc  ficri  potcIL  Hia  prxvie  conftitutis 
fu 

ProbL  L  Data  vi  imprejfa ,  ejm^  diriBiona 
horizontali  AB^^  altitudint  AR  {^  i;^.  ped.  ) 
determinare  amptitudintm  jaaus  k  G.  Sotutio :  Cntp 
in  parabola  fint  ab&iflk  ut  quadrata  (emiordinatarum, 

Aa  &  •  fivc 


5^4  SiSun.  OfmVH 

Scbol^h  SiEi  ^   GOtGH  ^  QQ^   « 
Ei*  ;  £G*  ;  fict  alremaiido  .  £  i   «  G^;  4  ^#* 
C    GH^  K    Q^s   ^G»     ;  prouidc  6  £ G*     =5  G/f 
K    GjQ,  itidcin  crit  4£/^   =:    £f   X    Gjg  i    mm 
proportto  cft  racionom  jrqotlitas, 

,  &60/,  li,  Qu«  hoenfqiie  di^i ,  illii(lr>bQDt«r  lii- 
qoeoti  problcmatc  1  D^  ^miw  curv§^  ^  cctitro  vu 
TiUtn ,  sn  qnavu  cttrv^e  punBo  dttermmare  vim  teturim 
f€t0tn  I  y  cekriuuem  profedio^ie,  S§la$ie  ;  Daro 
^Qoris  area  coiasvis  CQrvc  daror  ope  GeoM,  dreoloSy 
qai  car\'am  io  dato  pQoflo  o(cQicrar,  Datoqa^  cci!» 
fro  ririam  dator  cborda  circalo  oicolatore  inrerccpta, 
(eo  chorda  i  dato  carv^t  pon5o  per  foctm  pr^nfietis^ 
f/L  4d  alterom  circoNris  peripheriss  pondom  tennin^ 
ti ;  b«c  doeaiur  primom  1  poQct  eelcntis  corporis  ia 

CQ 
qoiCQnq;  CQnr*  rcrolo^  inr cnicnda  cft  (  n«iii  V^  — — 

^  f  9»»  Sehoh  Ih)  t     Invcoitar  «otem  opt  perpcndu 

cQli  in  tangcntcm  dodi  (^<  I790>  ^Qoddata  corvo 

tibiqqc  datop.     Iftad  «i  vitn  ce^itripetttm^     Ai  eeleri* 

fMtem  projfBi^wf  qaod  ftci^  dabit  eam  (  pfr  mtte  dl- 

&$  )  qatrtt  ptrt  chorddr  9sc,    Atqoc  bsc  genmlis  cft 

jblQfio  td  omnct  corvts  perripgens.      Mirvm  fm» 

(  fcribir  Noftcr  ) ,  ^9nn  ufus  fint  tbeoremta  b^e  ge* 

fier^fiOf  qn^  ad  cajus  particularet  appUcatn  plurima 

nlia  prifffent  £?  eleganfijjim^ ,  ^  utihjjitfja,     Sic  qtto^ 

niam^  Ubi  ftfofuf  fif  in  circulo  cum  vi  direBa  §d  ceti^ 

frum^  dHfiilm  vis  ctmp  f^geffte  tvadif  rtBus  ^  ^.^borw^ 

4a  ,  quarrf  circuhs  ojitflator  ^tfcindit  tf  direBione  vis^  efi 

fp/ufs  eirctiii  diavfeter  (cvimpfr  cjus  eefftntm  tranfirc 

^<:N^?f  fi^.qulvis  cirpuhis  ubique  fux  ipHgs  otciilator 

(Jf  )  ^  faci/e  fx  f/Morei/tatie  e^ipofitis  derivatftur  fa  em^ 

ifh  I  ^!9<f  WC0  yirff  tncfffunt  crrcularium  prodidit  HH' 

gfum  f  (?«m primis  //*  borfibgi^  fup  ojcillaforio. 


N 


Di  fmtu  in  fi^i^nihus  tcniciu      %6^ 

ScbcU  ilL  Ad  p«CQliam  rolQtiones  qQOd  «ftiliet» 
e3ct)ll>etitar  ec  fi  pectiUaribQS  cQrvaruiti  naturis.    ^vt 
in  cUipfi  jacet  pQndlnm  i  inter  S  ^  &  £  /    in  faraboU 
eongrQtt  i  CQfH  S^  in  iypiriota  jacet  .Sinter  i  ^  Qc  E 
(  pef  Ge&tn,  )  *       Seqaittif  :  Si  ptojeSionu  telerittis 
ianta  fit )  qUamatn  carpus  §  tbto  projeifiotiis  ad  auiruM 
Uirium  Cadeudo  aCqiurerii  nimi€nt$^~4udem  lii  Cemripeia^ 
defiribendam  ejji  parah^lam*     Si  ea  celetitai  mincr  fit^ 
4tUipfim    Si  deHique  majdr  :  bypetMam.      Sed  rtm 
Univirfi  tatculo  difnirt  opirofius  eft  ^    qiiom  ut  fetti 
iytcnei  po0nt  i  tecito  noltraiti  Makd*      £t  Boskovi^ 
ibiui  i  n&u  vaiat ,  (cribtt  ^  in  Itujus  genetalisfolUtionis 
iCttfidetatiofii  immorari  dttnitis  ^  ix  qua  ad  partieutani 
iajits  multc  operofiir  eft  dijieitfus*       £go  Veritati  haie 
«lariffimt  ^  qaii  Tyronibus  propolietidlb  tntiltutti  it^ 
hsfi  i  hodiequc  inhirreo  i   forte  •  *  «  «    SaffiCiat  lif-* 
tetti  cogtlitio  bifltica ,  cttiui  rertiinifcentifl  Ad  mitum 
afltctum  apprhne  n^eArii  e(l<      Pbilofofbtca  ^  Ctd 
T yfotiibQS  perobfenri  habetur  in  t^ijfhrt*  Boskov,  de  ' 
fmu  cqrpt  aiin  in  anti^*.  imtnobt  i  itt in  in  Stivi  tbiitis 
Scbifffl  di  motu  fryiSi 

$4  19$«  tum  \t9fput  iUipJtm  d$cuff$Hi  A 
ipfidi  funm4  difciftdit  |  motuf  cjus  idintidcm  dc* 
iilitatuf  X  dumqui  ah  iftta  afccndit  ^  fcmpir  rnaf^ 

datur.  Nim  Ctmptt  M  ellipfi  pefpendicula 
iti  tatigentes  dettiiflj^  decreicottt  prd  ntione 
iitittiinutarum  didAtitierom  a  fbco },  proinde 
com  Ct  i  a  pt  P  {§4 179«) » ^^  dercenfu 
per  orbitam  elliptictm  motum  ^ceelerari  ne«" 
cefTe  eft<    Contririum  obtinet  in  «fcefifi)  } 

Cotott,  1.  Proiii Je  in  icfpotii  Jifanjit  pif  iUip/nn 
i>k  ptojiBilii  ^  If  tmmfiU  cmj^irdti  dihii  fub  MUgu* 

U  MUia  (  i^  tiJiJ  i     iu  afunfu  M  mgulc  abtujh 
(ibid^Hah^^  -  \       Circtt. 


yr  ■ 


motti  «auabili ,  fed  celeritatQ  finalf  percur* 

liPiV=5  ^tl^^  3Ift^  'Porro  cuin  ih  motu  «• 

2"uaDiii ,  pofita  celeritatifip  lequalitate ,  jfpatia 
DC  uc  tcmpora »  defignabuntur  (empei^  per 
AM^tlAC^  quibus  ceniporibus  mobiie  m^» 
ftt  accelerato  decurrtt  A  L^  (ff  C  f.  Ciim- 
aue  in  piotii  ^untfarinirer  jujcel^r^tp  jQ^atia 
ptif  in.  ratfbine  ^diipllcat^  tebbb^um  ,  6ct 
21  L(CI  :=;  Jkf;  JC^  .  £ft  vero  ^x 
tjtpotb.4li  AHs?.4^li  Aifi  aq^M-oind^ 
4>  M^  ^  41^  M  4.  if  9  qiiMp:.Yiilorem  \n 
priori  proportiote  fQbftituendo  ^  ficc  :  4  JLs 
ettai  4L  H  ANi  AC%  i  tlACt  ^At 
rt  €1  m  AL  H  ^z;  (  namfaiStiup  medio* 
nnnarcO.  Tum^uerlnque  dividehdo  pet? 
^I,tfabebitur^Ca  =:  C/  >*  AN.  Deni- 
^ue  fiiiaa  arqualiiioltpndo  in  proporijonanii 
tntANi  AC  :=:   AC:  Cl.    Q.£*D. 


r.l.    .,*       •  ■  ,:••.;..    ,r       '^ 


$^l,-l  Thedremti  hutc^  imiiiim^  tiifte»nm« 
fom  %  Dofmnico  Cafpno  invcnturn  ,  cujus  hodic  frc 
f]*?'^:^^'^^*'^  ^^  iS^^^n^is  pilis  ignivpmis  ,  .  vulgo 
^i»»,  qiiw'  prinuirjedfrc'traditu|  Coms  a  Mms^ 

pmA  mmituf  Semi  -  ^rcMfo '  Torriet^m ,  ^auf '  eitittw 


^  I  <  . 


&ioi:  IL  ,Mc^ac9Wc  iiucUig^nt  omnes  cfle^C 
^  ff/^^^^^rdmatj^ ,  :<^  .C7  =3  4 E.i^kfciffti.    Qutv 

re  /f-Veft  paramctcr  diametn  -^^Rj^nam  qu*vis  ter- 
s««  ft^iknaiif  sd  ai/d/am  qaamctinquc  ,  &r  r^. 


Li  metu  infd^onihus  contch^         $67 

iejirihum  Mreat  tempariha  pn^porthnnUs,  iy.  deferf* 
bere  debcnc  j  nam  iftndi  in  quavis  curva  ficii  dcbcic^ 
docni  §•  I79t  CoroU.L 

SehohlU   Jflm  qnsfitft  allqtiot  cxpcdtam^  qiic 
uGii  erunt  in  mctu  a/lrorem,      Q.  i.  Otr  Fiamtte  in 
tlUpJi  eirea  Sokm  revoluti ,  coiifeiU  periodo  Ji/a  ,  7iofi 
eafdem  inter  fixm  Inerere  videntur  ?    Kotflrunr  cnim 
Aftronomi  :  poft  plurium  annornm  decurfus  altidi* 
jnnm  orbit«  planetarix  pnndum  (  aphelium  vocanc) 
non  casdem  inter  ifixas  hdtrerc  »  quas  inter  hsrebac 
alias.      l^,  tribucndum  iftud  acciVi^/rtfrftf  cauflie;  (ci« 
licct  2  mntua  Planetamm  omnium  attradio  eorundem 
motus  £en(ibtliter  pcrturbat  \  hinc  apbciiorum  progreC 
fio«       Q.  II*  Quom^do  peties  Flonetas  fuadrata  tempo»< 
rum  periodkorum  femper  Jhnt   nt  cubi  difiautiarupu 
9«  ad  rigorem  loqucndo :  funt  ut  cubi  diftaptiarum 
.duntaxat  mediarum  ,  in  qoibus  affefiiohes  ellipfcot 
conveniunt  cum  afFc^ionibus  circnli ,  qui  defoiberc* 
tar  media  illa  dilhntia  pro  radio  aflunipta.    Qooniaoi 
vcro    orbitc  planetaric  admodum  parum  exeentricet 
funt  (  nam  ,  Keillio  teftc  ,  cxcentricitas  t.  c.  orbitc 
Telluris  complcclitur  fere  17.  earum  parttum  »  qu«» 
rnm  t  ooo*  complcditur  diftahtia  media  )  ,  (iimi  po* 
teft  :  casdem  cfiie  afFefiioncs  orbitarum  pUnetariarumy 
qu9  font  circularium ,  ae  proinde  pojita  lege  attra^io» 
nis  agentk  in  ratione  reciproca  duplicata  diftantiarum 
eflc  qoadrata  tcmporum  periodtcorum  ,  iit  cubos  di» 
ilanciarnm,        Q#  II!.    Cur  Plaueta  ad  diftaneias  me*\ 
dias  deiatij  in  qnibus  crdera^funt  afTcdkioncs  cUipfeoffy 
qoae  circuli ,  non   circnlos   defcribunt.      ^    quia  vic 
tangentialis  cum  centripcta  non  confptrat  fub  anguio 
.  reilo ,  qnod  tamcn  circulo  coniiciendo  neccflariuin  e& 
Cg  docoi^.  iS^*     S^atuendom  itaquc  :  nonomnes  ^  tkd 
fierasque  cllipflum  affefiioncs  in  difiantiis  mediit  cas* 
dcm  cflc )  qu«  funt  circuloi  um.        Q.  IV.  Si  ccnjpi* 
raM  virium  Jut  angula  reSa  faeiat  ad  defer^tiotum 


tirettH  t  fUid  ifi  \  jucitfa-Uiha  (  hibetflr  itiMll  i« 
itttflioid^  &  ihAmo  ttmltx  elKjoeleie  pttiiao  ^  h«e«  in 
ipfidlbui  ^  «loii  dtfcribitut  cirMt$  1  ^i  quii  ddicil 
Velocieai  prbjeAlonls  rcqailiti  id  drculutni  Q.  V« 
i<  prd  iiAtia  fUaUiiiafe  4ii  €entripH£^^  itttHque  pr4 
i^aria  tclftitOii  pr&jt3ionii  itaria  ifi  ^flntairum  cutitido 
C§*  17$'J\  quomdo  in  Utfaqm  apfiit  ^  ubi  diurfd 
i>abetut  V  Vif  iiHtHpita  «  &*  prdfe&iUt ,  iadem  ifi  «r« 
hitdt  infledciQ  }     ^.  quii  ntnt  md§  a  qUOniiidti  %iii  cifh 

ttipet(f ,  tf  profiSUoiiir  i  Cti  veto  iHifti  ab  atigtilotum 
vatietati  peftdet  cujusvii  eutvc  ittilexio  ( ibid.  )  j  qao* 
rtlm  Hno  defidetite  compcnfiitio  fielri  potcft  per  alittd« 
Q.  VI.  Si  PlatUfta  in  illipfi  tevotutui  utgeatut  Vt  cctf 
ttipeta  agHtti  pra  tat*,  inv*  dupiii,  dift.\  qUi  fit  ^  Ut 
iiM  Jubindi  iu  dnttUfn  fuum  detabatur  \  e<  c«  Lutia 
•iu  tirtam  1  rilit^i  Plauetii  ptimatii  in  SolitH  ^  JecUn- 
darii  in  ftidt  pttmatiot  }  Sane  ium  t>U  tinttipita  in 
altijfttiio  otbiitt  iUiptiCd  pUuSo  tmitte  fit  efficacitatit  ^  Uf 
flanetam  aecedeti  cigat  ad  focum  ^  fitti  iieutiquatH  pi* 
titii  i  ut  in  imo  femitee  fu^  punQo  tecedat  a  fbiOy  uhi 
pto  quadtata  itttmtm$ts  diftaittiei  %fim  cinttipitam  auge* 
ti  neteffi  ifl.  Quatifa&a  tantininiit  accejjione  ad  fb'. 
aum  debit  fuiiftdi  in  fotum  defabi  f  nequi  eUipfim  itu 
agtam  difiribiti  pMft*  M«e  eft  (btenilis  flli  obie« 
Attlo  eostim  otnttltim  ^  qot  tfnptini  pkdds  idver* 
fintdf«  9<  <fti  noti  ibntio  I  eft  in  inflino  (etnft* 
«llipticir  ptindo  mattima  vk  ttntripita  >  it  fimuttna* 
itima  ift  iNanitet  Vitocitm  i  iC  pfolfide  kerttiti  tnaxiM 
ma  ak  tmpofita  i»  tenttall  ^  ts  iaugtutiati ;  cnjtii  S* 
fiOid  tintoin  it>cft  ^  tit  id  eentrtim  virttini  rendit  « 
frt  potioi  Ptifletim  ib  eodem  ivertin  Std  hiotf  ^ 
bojtir^ue  fimilei  ob)eftloties  alliS  ad  ntoium  afttitmt 
iboiidi ,  &  ipiii  BoskivitM  iftrbii  diltiim«  Jmttf^ 
tmi  f  mkibidii  fttfficiil* 


Pa- 


Dis  m^hl  gravilim  teyr^rian» 

f»  !^Ci    ^yaifii  0^ia  plriygiid  (h^U^ 

fee  ^  ic  gratitAtii  dire^ione  id^ciilmm  p^0^ 

Mmh^  tujmt  umgtnt  ift  iffo  ff^tfiHftHif  ditctH^ 
M  B  (  /%«  5  !•) «  Dff^i  Si  gra¥e  projtci«ttir 
fecUndiim  if  B I  8e  interei  ti  gravimis  ilf-»* 

fearur  feeunduitt  A  R  ^  ufgebitui'  g«intqh 
iribiis  diverCK  rationis «  qaafi^qa  ahere  Mf«w 
.^iftc/  e(l  ^  tuefkrdHi  elcera;  ^  qiUTe  ttiobSU; 
'{ple  anifarini  projediooe  inipiikiMft  fioj^uliir 
it^aeiibas  fempuicajil  deftrtberee  fpetie  W* 
qualid  ^C|  (?»$dMe  Mceifigniviteie^adi^ 
it%  ferie  fiumerorum  impariuro)  liipe  utris* 
Qtie  viribbriflimi^ftimeue  debet  primo  Mm- 
fiu(l:ulo  iii  f  I  alt^ro  \n  K$  qusi?  puiida  ticMl 
lacenc  in  eadem  ftJ^  ($4  98.)  »  Ted  in  eur* 
Ve  psr^MkSk  N^m  in  moiiiaiiiformiter  a«i^ 
eelerete  Q>atia  funt  ut  qitednita  tempo^tMi  |' 
tem^ote  eutem  diiignantiir  Bnef s  AG^  A  P' 
(  cum  in  motti  «qitetMli  fpatia  fiht  ut  ttm» 

\on)i  fiett  AEi  iff  ^  dC^i  A  Di  m 

ti  i  Mfy  «    Surit  Vero  AS^  6cAi  ibGAC^ 

^^  :  Mt^  icfK  remiotdiii4tde'^  ptoiiidb  i)u*' 

drau  {emiordifiatarum  ftlnt  iti  titiorte  ab^ 

ciflarum «  qu«  eft  proprielas  |N^t»olai  ll** 

behiis  dR  p»  diametro  1  iTM 


^jff^       ^  StamJU  Ofm  PI&  •<& 


N 


SchL  L  SimiUcer  ^  psxf  opfK»fitt  defcrftcrar 
fiiibolt ,  fi  corp^  obliqafc^A^itfiar  iecmidaai  di- 
fftfiionem^^^.  Nce  modo  fi  ^ilifua^  (jsd  etUfn^»  # 
4lprN#iMMvAlStdireffiofrt}c£Ko^^^  m^ 

ttboiam  deftribi  necefle  eft.  Coniiciror  iftnd  proDO* 
done  etdem  ^  qae  paaio  mox  ufi  fiimaf.  Immo :  6 
€|[^piii  0<^  qnidem  projid.i  (ed  alia  vt  (ecnndwi  ro* 
4Jftmhorizoatalem  ibripipohafnas,  ita  ramen,  tiria* 
teiii  ectim  ft  {rivfcifif  delcendat,  iteram  paraSoft 
diftiibetnr  4u  hterviUlo  uou  Mdmodum  magk»  j  ^iure 
cpAi  iscigtm'.^^^fif  sircuU  urrtfirii  arcm  pco  re€ttf 
lioriiontiii  ddjp^pm  baVeri  poflit,  gravcqabdvis  *€ 
lcifi  U9U  lumif  alto  defcendens  perabolai^  ^e^f^ibit  in 
fcypothefi  terra^  moCji;.  Sed  enim  :  JuMunr  faraboli-' 
iiM  iiou  oifervamm*  J^id  ita  uon  ?  jA.  in  caaflt 
€(l*/<]|bod  tini  eum  terrt  horizootititer  moVcamar 
iitHli  oMimiilii..  Sicneqae  li  qais  nifi  celerrter  pro« 
falfiiircaoomoitt  etfMnniai  iiioveitQr ,  idyertir  lip«» 
im^  jC^  fiMnmkKcttDifi  demiflhoi.  eanriia  d^ftruMrei 
«tf ry  W  wyn>#  6>tftetor;  m  ligoti  ooptetnttti^  « 

Scbol  iL  UxQ  corpdtnfi  /Mif^ »  <ttt  lorit&Ofi 
utiter  projeOorum  theorii  non  obtinet^  u&i  five  i^riif 
t^J^niia  tAotnm  impidit »  five  gravH^magnitudo  ^ 
gmt  dire8i$  non  eadeib  pcr(iirerat  Nempe  :  cnrva , 
4fnm  prol^dile  defciPiMt  ii>  tere ,  plurimnm  tetidit  d 
ftur§b$k  y  if.  Mcmd^  ad  fhrmam  Irfpertolse  ,*  «mtv  ui 
f^mn  quandam  e^fmputkam  aeeedeme  i»  iufnntmei 
0tiH  tdipiam  cmg/ruani  \  fuod  quidam  amdit  poeiffimmm 
in  gtohi  minm  pofiJiramHmf »  vel  uii  eum  ingenti  ve* 


nk  aeeepta  perpetne  aiifutd  detrabit*  lea  Botkovhbhtt' 
£cdcm  tlli  cetfii  rcfiftencii  efficir  ,  ne  fiaida  e  vafii 
cmmpentia  ^  iaV  cMiB  t%  ingnftii  cinilibai  direfttet* 
nciid  horizdiutm  iiQcli^i  profilientet,  corvas  atome 
.  .    /  ptra- 


f 


i 


B#  «i^lif  grmAum  urrtfirikm         ift 

^artDoIicas  dclcribfliit ;  (ed  diif r|Xtf  ad  pirtboltiii  if» 
ccdciucs*  Cuca  ^avitaum^  ycro  Itdem  MQyf[  ^^ 
qiienria  :  cum  grdvitoi  eonvergat ^a^  Tnra  cnurum^ 
4yrffiat  m  r^ifit^e  .recipn,  dfflic.  Sft^Mnfh(Ji§fki^ 
ket  deJcrHi  arcui  lyfirbgla  ^/jf^LcUijijm  bab^^ 
iurn  in  cciffro  Tcrra  fro  var^q^^^kcit^t^  j^4«M^.|Nrfr 
}i(lioHff',  qiut.tameH^m  n<^ris  fr:PJtSiotiibm,r,$HM,n^ 
jfcrimur  infiiper^cjc  Tcrr^i^  P^i^P.^^  *<^  ¥^  iHHff^^u  tj 
tUiffini  induca$^qt{d  tamefi  oh  ifftviaHcm  d^autUm  «4 
terius  foci  a  vcrtice  froxifm  atteri  /oco  ad  pmraMmi^ 
^cceJit  qffam  proxime  ,  if^  fum  aUiffis  iu  immfHpim 
^blongata  dejmit  tandem^      ... 

^  .  ScboU  IIL  $i  arcui  jHKG  (igibtcndatisr  chord« 
/f  G ,  dcfignabir  pa  dijfaimiam^p  reda*  uAm,^m  con» 
ticSxt  ob)c4iam  Kricos  Cam  fcricndO|  dicitiir  d^fimh 
tiaJ^mUciur,  Qpod  fi  ab  objcfl^  (cu.  fcricatc  ,  fia 
fcricndo  dcmitta^or  pcj^cndicoliMn  td  ber|Mnsc«i  > 
ifttid  dicetur  altitudo  jaam^  JK|;ft4,  tutcfn  RCt  uicc^ 
^crpcndicalum,  &  fcricmis  /  aot  fcricndl  loeipm  in« 
(erccpra  ;  audit  iorizo$tiatff  dijlautia  ,  qak  ctiam  mn» 
pitndo  jaSut  in  horiawnttU  dircdionc  yo^^i  iolft^ 
Porro  cxpericntit  certum  habcmua  :  mtximtm  tm* 
l^iitudiocm  jtdos  obtincri  fub  ^iftfiionc  45^ ,  coc 
paullo  minorc,  Dlrcdioncs  $iim  cqQtlitcr  t  4$^  4|r 
fttntcs  (  c.  c.  fub  tngulis  6q^  ,  &  )o<'  ,  tut  70^  1  tk 

}\o^  &c. )  ad  candcin  jaSus  tmplitudincm  grtvc  dcr 
crunt  manentc  cadcm  vi  imprcflt ,  h.  ci  mcnlttM 
pulvcris  pyrii ,  mancntibas  codcm  lormcnto ,  codci^ 
ijuc  globi  pondcrc  f  hioc  cft ,  qood  idcm  jtdot  doir 
plici  dirc£lionc  ficri  potcft.  His  praevie  cooftitotit 
tit 

ProbK  U  Data  vi  irttprejfa ,  ojm^  dk^Si^m 
iorizontali  jtB^^  alsitudim  ^  R  {  zi  n5*.i^^  } 
determinare  ampUtudinini  jaQm  ti  0.  Soluria :  Cnip 
in  ptrtbolt  fint  tb(ciflk  ut  qutdrttt  (cmiordintttrum» 

At  ft  •  '   fiv€ 


J 


L 


§.  aoOk  In  utroqiie  pcnduto  tlterfiar  Ug 
U  hini^  ,^Qc  ilHnc  prQC^ruenes  (  qu^  Bonf^ 
fi  filufn  .e/Uco  fup ,  dimexe «tur »  &^  pondu» 
laprui  6m  relinquatur  )  aodiuite.  ^^ettDwi » 
$at  vibr^nhnii p  quae  <y2i^M«iur  i!iiht  >  fi  ebdem 
tempore  a^folvantuK^,  rel  hMtfyJloctrbfht ,  fi 
breviifimo ;  iftud'  enim  Latinum  (bhant  to^ 
ces  Grxc».  In  pendulocompofiro  ji^u^  Tir^ 
gx  pundum  »  in  9U0  fu^latu  c?ter||i  ^PAn* 
2eribii>  locandum.  edM  grave  upicom  »  uc 
iobritteatiir '  ^i/ff^am  fimfltx  tampQfit^  ijitin^ 
mim  I  Tocamtts  anmm  a/iilUtipm^ 

'  Cirotl.  bmne  pendolum  compbfirQm  re^aci  pol 
toft  td  iimplex;  quocirca  '^u^e  in  ftndnh  JHniftiti^  €$• 

4tm  in  comfojlfo  hcum  babtata  ,  t/i  mcejji. 

ScbpL  L  'Qnodcanque  pendulum  of^illet ,  parct 
Hfud^inoveri  vi  g^aviiattf  rej^thiv^t  \  riani  vi  gravi^ 
Sati^  abjbltit*  movendulh  ^eflct  liAea  ^d  horizomem 
perpendicoiari.  Idem  efto  judicium  dc  o(cillitioni^ 
bus  tton  jaai  ope  fili ,  auc  virgc ,  fed  iu  curvo  eanali . 
facrisy  10.9PO  cx  parrc  opppfita.poft  imum  fvnctam 
babaanir  ctifVi  pror(ul'tfquUi)/ac^miHsfriorit  & 
Cmiliter  pofira.  Quare  ifiis  appUcari  potcrttQt}  qos  ad 
ftudHltrttm :  aftillationct  d|c«m«  ^  ^ 

ScboL  It  Qusvts  curva  confiderari  poteft  rtn- 
quam  compofita  cx  infinitis  ltneoli«'rectis,  infinite 
parvis ,  quae  exhibeam  Ipngitndines  planorum  tnfinitc 
pirvonmi  (/l^  59)  «  Hinccflti  quod  ,  cum  de  pla« 
Hts  indimtit  agerm  f/.  143.  ^fiqq^t  hqic  locb  rc 
Anrnvi ,  qi^t  ^i  J^atia  ,  '  ctltritattt  ^  BT  ttfitpara  dt- 
Jttnfiatm  pcnrttticnt.  Hcc  iblicitc  notanda  b^cvitcr 
comigtttbo.  Oibiib  prope  tbcoiSa  pcndulorum  hidc 
•  •   ^  nipc.- 


th.mtu  grmimB  Urr$ptwm%         379 

Probl  III.  Data  vi  infpr^§ ,  V  mffUmdim  >• 
flm  i^urmimri  akimdiftm.  ||t,  Itenim  «*  ngciim 
Mrtbolc  habetor  ^£<  ^X  »  fl*  ;  R<H»,«ni 

tede  ^  X  »    — I'     ,    -  f    .  Numcric»  ^  |t  s). 

'  '  ^  '^rqbi.  iy*  ,P^<«  ahimiiim ,  Sf  M^ifKMf^^  jMi 
£Fitf  dmrmiHAri  quantiUitm  vk  frpcliiUf  ,  fto  rinV 
«im  jd^a/fi  (tibu  ,vi  projeQtODis  «rdnfid cndll )[  id  mi 
ntm  terfifm:  Sohti:  Coin  mobtieHapft  Kbcro  Um 
tTft  l^  confictot  'pedct  t  S  i  ^«pcrictiMr  l^tttmi  «odcfll 
teiDporc  iMtu  (  DHilbnni»  pfoieai^mt  4ccttrrl^ti4iiii| 

(roindc  -^CJ»^     ■■■'    '.   i  A;  -^ C  »  $^    ;  ■<  f>"n^ 

lii  namerif  pribjfibo»  -rfC  ««  ^i.^— . tSi  ^' 

Qncre  mobile  impellttar  ttnta  vi  imprcflk  ,  oncnt^ 
ftlt  fiogtdis  bio^tciii  finmdif  ometirctAr  iol  ^PedcN 

'■-  I.  197/ lliedr!»  ahWotfie  BiUimrc«  ii« 
^bec :  H',^  j^rjum  pnJutmmr  Cfig.$t*\^  *fi 
fimsm  A  H  fiUilrufU  if/mt  AL)  Cv«  «jat 
altitadinis ,  m  qo»  delabem  grave*  4MqtUMK' 
ret  tamaai  projeaionis  velocitatein  ,.  qiianta 
grive  proieaam  ferretar  per  ^C»  fi  ^jP*** 
Vitatis  non  tthp6diretur  )  |  )Sif  A  N  .*  A-C^^ 
ACx  Cl  pm*  qao  tempgie  corjs.quqpta 
«ccelerato  percur^erec^^ii"^!.,  eoaem  eeniporc 

A  a  3  •     m,ot^ 


Ul 


■W*o  »5i»Wli ,  fed  celeritare  finalt  percar> 
*'^?.^»  dupl?»»  de  if  l.  (  §.  Itfo.  Onilf 

aabilf ,  poGta  celeriratm|i  leqoalitate ,  {piitia 
nc  at  tempora ,_  defighabuntar  teicpjBiM  per 
A  Mf  8cJC,  qaibiu  tent||oribu»  mobile  me- 
tn  accelerato  decarrir  J L,  Cf  C h  Cum- 
O^e  in  (nota  jiniforipiter  ai;cel^at9  (patia 
mt  in,  rat!b|ne  '^upllcar^  tetnb^fum  ,  6et 
I  t «  C/  s  ^itf^  :  4I  C>  .      £ft  vero  «x 

^f^^  Al,  M  ^i^,  qMiflp;X«iorem  in 
JN-iori  pMpertioteorebditttefido  ^  £«c :  ^  Lt 
^'a  ^i-  H  ANtlACt  fieACM  M.ifit 
*  ^i  n-AL  M  ^/7  (namfaaammedio- 
rom  ftc. )  .  Tum  •'utrlngue  difidehdd  p^ef 
Jl.Wabebitar^Ca  =-  CI  h  AN.  Deni- 
9ue  fiida  «qualiiiblifn4o  in- propor«on»n>j 
tmANi  AC^  AC:  Ch    Q.£,D. 

-  -Wi>ArX  ThMrcaMti  bai^  iiaiiimi  iliftnHnatM 
tnm  ■  Dotmnieo  Caffino  inventam  ,  cujas  hodie  fre- 

A«  ih  GeiJria  arlitAi  ffnehendonk  A  \kV81    Noti- 
FMlcfc  «nitar  A'i»«-«fr<^<»it&/-r«i«ii;»  Auffeiwell. 

^-If» *;?'*/*"''*  ' -l^  ^'  =  ^iJ.n^rcifli.     Qu«., 
r«  /WeftpSramrter  «liJ.netn  ^R^Mm(iu*vi$  «r. 

T*.  f^.r*"^.'^  «if^JpuM  ^aa<n<ffcnque  ,  ST  m- 

'  '   "      :  '    ■«■■■'■      ' '    --1  '4  '    ^n.  • 


•'.'n  j.  4. 


^  4        ■ 

^ctcret  Ofcofii«cr«  Utm  r(tS$m  «ppdlabinV;  ^  HodtQ 

Cn9ll.  I^  Qyth  jtC  diRgntitl\ntm  &ite8ti6ini^ 
foxia  quiin  c.  c  globtti  vi'(bta  pr«|edfli  imptiifti  «B^ 
m)  C  I' vero  iinetm  li^fiif' rei^akt.  (Iijic  ^n!AL 
^anmafo  \d«fl«ait  globut  t  linea  direfllonfi  )  ;  ml» 
Hifeftum  eft  r  menfitr^^m  frtijtSioftk  ;HiiixaM  tlriffA^ 
mk  cert«  raf ione  definitain ,  ^  lifuam  kffk  nj^ 
t(^'ir##  C9ntin»€  fr^or^onahs.  -   ^»  «' 


•  f  I"» 


k  C^roU.  IL '  Ut  gi^ire  «re«m'  parabol?ciiitt  jfii 
hnt ,  dcb«r  celciritai  projeftibniy  ciTc  tanta  ,  quan^i 
•orpua  icqiiireret  libere  dtcfcendenclo  p^r  qt(a^A 
partcm  pirametrt  pertincnttirai  ^m  dBiniectufir^  'wA 
iTinfit  per  punfium  projcttiMi^  -'        '* 


.*r  «• 


Orpff.  Jlf .  hftncnfe:  eadiem  TdoCtfitt  pro}eCK(|^ 
nis  maDct^Zf  conftahi;  crgo-Sc  (^Npafametcr  mA 
nct  conftani.  Quare  utcunquc  mutctor  drrcffo  pr^ 
je&ionii ,  eadem  rainen  parameter  qmnibui  pariboUf 
€adm7$  vikcltato  dtjcrifti^  commimii  crit.;  *  # 


*  Cora.  IV.  DiMntti  fb^i  a  vcrttec  aJiOQitttr  qtiaiS 
tft  parti  parametri  (ftrA&tlftf.)  ;  cr^o  v  cx  A  punl 
Clo  projeftion^  radio  i^L^cferibiftlf  circulor,  (^ntf 
pcr  foeui  quiromni  piMbolirum  (tad<m  fri^eSidfUi 
etltritate  dejcriptartsm  criC  in  peiriphertc  dt8i  circoIi,7 

Sciifc  Tlf.  Probl.  L  Deurminirefnenfltratit  pr^ 
jeSiofUt.  Soitnio.  Si  ali^eBnm feritfis ^lf  ferititdutli 
fiit  §n  tadtmUneaboriaatitdUfi.t.  \nAl^fig*  5^.),  cxplo«^ 
(b  femcl  tofmcnto  (blicitc  notetur  dtrcSiO  pro)efiioi|i^ 
j4B\  fivc  angului ,  qucm  formit  Imci  direetio>iii  cuni 
hoi^zontilv';  tuin  tneatdr  exaSa  Aicnfiira  diftahti^, 
^ly  ad  ipitxtt  delatoi  cft  globtti.    Expimfio  ^  cri« 

A^a  4  •         gatttc 


ponil  4^    jAoifii  iLiilCm««gfilu  ad  ^,  <k  1»  ttenw 

|«fi:«nc  Ifttera  KJ,  fkAB.  Hit  cognitttfii^r  propor* 
fb.l  iBi  ;  vrf^  i;l  ¥<  Jl  I  .^^  b,  e.  qii«r*mr  rcrria 
jwoporciomiis  td  diftas  )gj;  ^  ><£}  liebir  m  tldi» 
llfrirafii  projedioois  infnfiiftni  AVi%  11«  S»  #f^ 
0mn^mim  4hiH^  (  «nt  hQmiliore  )  /(74^  confiim 
jfim  ikf  e«  c  in  0  9  dnda  pcr  O  linea  $i  Jborizoniem 
fffjxeii4^q|br^  |l  0  /  explorctur  dtftftnfit  A  0  >  tiefi» 
fUirof^Ot  •Iter  engolQf  QAl(  mm  iUe  «d  Z  rffioo 
oft  )  ;  bil  eogoitis  invenitor  AOI  ^  proindcque  & 

S'  *9  ](oiajpl«aieotaai  %(}  .dnm  rcQos .,  (ifr«  ang;ohii 
[OM^  Sioiiiitfr  «i^oliti  AB  Q  fiKiie  ki^enieror» 
m  ob  p^n^hfiJ^  J„  ^  Ai^^iVc  dcbec^M  engolo 
^if  M^  mljnoaific^  6j$plor«fQ  BAL  Dstis  teiw 
lAi  in  ^lo  ABO  mgfiri^%'  dnobqs,  fk  Uferf  4Q 
ifmm  fn  Ttigommetriam  definietur  B  0,  4c  ^  A 

SrfOiO  qo^retor  ^i^.^prof^riiooeHs  |d  AO,  dl  AB\ 
^  dfiidirm  proje^ioQis  oien£iir«  (  i«   I9ff 

Probl,  II,   D^  pf4^i9nit  Mmfiars  4N^tf/ 
Jlh^itm    /'O  diHmiiuart  funStfim  piaui  iBim  ^  fl| 

fN4 ,<<M^ j[/9i^ Ci^. 5 4* ♦S J»  *A»*«o ^ q«<t«»«>r  ? tie 
f rQpartiQi^s  «d  ^N,  ^  ^^  ;  h«o  invente  def. 
glftdaii,  p!sni  pnnduni  M^'m  qoo4  gk>bos  inetdtc, 
fC.fi  omiiis  &Q,  pfragitui:  I  i^  A  lo<;iii  meehinc  belli« 
(^k^  $  ^  ^i  i\,  pknqni  iQcie||d«m*    Si  hm  w^w 

idm/lie0  uott  efi  in  eadem  bvrizmtali  mm  pfan^  ftrie^^ 

^  }  mg^ur  primuin  j^prfiffu^icphriier  i$i  HMeam  Ae%  • 
Hji^iamiil^tn  oifnfliFa  pro]f4Nai|is«^>7;  cum  (iiper  da« 

!R  proje^ipQis  menTiuM  ccMnti;uatur  /^inm  ](f»/i^kf  ee 
fgf ,  ut  btUS  ^^  C  perpf iid.iciil&riter  infijlUl  f  iano  fff 
rieodQ  /^^,  E)c  Cre^jo  WC  de(0ribator  ciFealos  ^ 
^luf  trenllbtt  fior  poii^im  N  i  fangente m  hibebir  ro< 
(Uai  <ff^  ^  ^  Ijnfam  4ii4^onii  he^leoue  isi^efini^f^ 

,.  fc'  feceWl 


k    ^ 


I 


2fff  jMiii  jpwtefff  Hmprtvfm        %7f 

tfi  D»    Odncfpt  voro  iyCD  dcrmtteatur  in  ptft 
mm  ftri«ndiim  rtda  l>  M  r^t^ic^Hs ,  &  parallehi 
incnfoFft  pir oitOJonif.     C/rr  s  r«^«  D  M  d^tinier  i% 
l^ono  fertend<»  pondm  My  in  qtto4  incidat  globoti 
ii^  Miifn  eft  311«  proportionalit  «d  /t  N,\(St  AD'^ 

£u9d  tkmvifir^mkm  fitftr^ftn     Enimvoro  dtt£b  N2> 
fthcbitttr  ^inm  JlND  to    A^^  ^DM  (  mm  oll 
ikilf ,  Si  jIN  piralkltt ,  ^ft  tngalut  ADM  rsi   t% 

Snto  Ny^ D  ;  taqt  angoltts  D  AM  ^4 tfD;  t^tn 
Kbo  ba|>eant  ctmdcm  iai  menfafamj^  ftilicet  din^j* 
AiQm  trcM  DB4i  proindt  AN  t  J D  ^  ADi 
H  M.  Q.  E.  D,  Jt  hm  mdctiiuf  Mi/Hc€  ^  ni 
»<irfnjii  horitmsMli  cum  pknojfhitndo  (fig  56  ) »  con» 
tiiicio  mcnrttrt  projodionii  cri^tor  perpendictttaritar 
$d  dfltuin  planum,  ^  bifaritm  loeetnr  i  tvm  c  pondii' 
ki(«etiontt  ^crilMUttr  circnitttt    Ccfcra  porag^n<h  liC 

£M  IK  Qttod  angoiorom  DAM,  %ANO 
#odem  fit  menfiirt  ^  doeet  0§$mnriti  ,  per  t|utm  an» 
galni ,  qtti  <It  10  p«ripheri«  eirciili  a  tangente  ,  dC 
chordaf  habef  pro  monfara  dhnidittm  ^rcui  ab  ea* 
dem  chorda  (ttbtenfi  i  ergo  m^nrara  anguU  DAM 
•ft  dimidiom  areot  DBA*  |i.  ettam  angulos;  (]tiem 
in  poripherta  eircoK  oomprehendttnt  dim  chprd^ ,  faa« 
iMt  pro  menrttra  dimidUim  arcoa ,  cui  ^utdeiii  thini' 
iofiftttot ;  irernm  ergo  mtnfttra  aMoU  AND  eft  di» 

nridiom  aroot  DBAi  ei|Q  D  WAl  =s   ^NJP, 

■ 

Prohl*  lil,  DlOM  f9Hffe9idfaf  meitfkra  AN^  Ah 
fifi»e  fkm  fmiBpJMfnd^  M^  iHirmiMrt  Imeam  4i** 
rtSiantf  ADj  vr/  A  d.  Solutia :  qttS^  ,  n?  prioit 
iMnfiiM  pri^eMdiilt ,  deftriptoqoe  circalo  ,  erigtto? 
f  dato  pondo  M  t^M4  D  paraiWa  monftni  pro« ' 
jeAioiiitt  Iftn  ?el  cironlttm  ueahit  tn  ponftil  do^» 
iMt  D ,  4c  d,  vel  (fi  feriendam  fit  m)  tangif  in  mU 
€•  #  I  f^l  d^ai^vt  circttlom  non  coming«t»   M  fmiw 

Aa  5;  «        9m 


I 


^m^  D ,  r«t  i ,  *i^.,qojbat  circBlBt  tpemri '  iitii  4 
f  iin<^in  B  ,  in  qno^  tiqgitQr  cir^^lqs »  dneimar  c« 
^  loco  machtnif  UJUftics  ^*  re^  &i  A-D  ^  ^^  j€  d 
ttvLtABi  fi  fenendofn  &  »),  qn*  ckbiuit  dtfiiki» 
rafail^  lifieaiD  diredionis,  Dm.  Sic  eaiin  ienipcr 
jnnfiirgcnc  ^la  fimiiia,  proiiidfqii»  mimfiirm.fr^^ 
l^om^  lum  dirtBiaim^if  Um^  Uffmr^^^m  ermHk 
trts  Qttfudute  propmiiimUf.  Nam  Into  t  /\toi> 
jiHti  o)  ADA^,  qopd  Ctpf»  .cyri^^i  cft;  cCg^ 
A^\AD:=i  AD:  DAf.  Mdfiki  £^lumAdM 
^  00  /^lo  jt  D  M.  (  mm  anguM  dAH  ineiufimi 
^  djmidiam  trcoa^ii  qjDodipTuin  diinidiiim  irciU 
A14  ctiam.mcnfiira  eft  anguU  ADd  '^  tom  «ngolM 
AMD  eommonis  ell  otriqoc  /yio  ;,  proindc  ango^ 
Igs  vf  ^  4^  p   p  //  Af)  ;    e^o  .crlaoi  ^lom  Ai  H 

y^  ^,  A^^^^^t  cqfo  4o)iii#  ooi  )tta  A  DA§ 
umiUa  fint  inter  Cc.  Hinc  vcro  confurget  proportio  \ 
*A  N  i  Ad  zz  Ad  :  d  M.  Quanqoam  qoid  opus 
^luio  ^DijtfinCuppcciss  vocafccZ  .  Qjitipendio  a- 
x,p:t  conppUtor  ex,{^  duci-^cd^  Hdi-  crit  altcrnim 
AdM  =3  alterpati^^N;  mi^^Ld^AMzA  ANd, 
htbcbum  cnim  ambo.ci^dcm  mimCNtrant;  ficc  A  N: 
4diA  Adx  d.M.  Illtio:  Pn^i  NB  ,  &  w4i> 
nsb^tor  ^lom  /^  NB  .^  A^^^  ^^  ^  >  a*<*^  ^I^  P^ 

ittf^.  stignlos  J^ // f/i  ;;3   ANB,  qh  «andcm  otriai- 

yiC  menifaram  ,    .q^pcirQa  ^  N .%   A  B  :si   A  B:t^ 
m.  .IVroj  Si  ex  j^m|£)o /i  srjgfnja  ^vcrdcalis  dp 
parailela  ad  mcnfuram  projecrionis  non  occurrat  cir- 
cpla  f  inflicium  cfit^  v^tea  /^k^c^Mmt  [me^fmrM  fun^ 
^ftm  iilstd  attiugt  ^Hm  f^jfi^  .        '  *  «^    -i 

.'. '.  •     '        ■  '  .  ''*  ^     '    •  "* 

Prabl.  IV,    Daertfilmrf  ,  qu$t,dilV^i9uilfi»^id(ii$' 

funiiiim  Attingi  pojffut     Sohtio  iii^ii^c(ts.  e(l  ox  prior^;s 

njiin  fi  yercicalis  e  datp  puncco  tVriendo.  erecra  cirea«. 

lt|ip  fic^ty  p^rcr  hinis  directionibqs  iiiem  punttuiai 

aqiagl^Uc.^  &t4i^gh^  onc^  ti  t^ei^xqntingsn^jix^i 

-    *  **  li« 


1«^  Illa4  noto:  fertiore  ictu^  quia  ex^^difiort  lofo, 
fcricridum  efTe  pMnctumMi.  fi  «dhibeitur  directio 
^  D  'y  ictu  vero  debiljpro  .  fi»d  brcviori.tcmpore,  u 
«^l  cra  w^«  

• 

$:'t9S«    H^rizontsUs  smptttuiiHis  J4Buum 

jtM^  il  m/unt  ut  fiuiis'  4^pi^^  anffil((rum^ 

^ti§s,  forsHdta  linuti  Mndionum  AD  ^^  Hil  AA 

$um  li^fs  bortzomsli  dfi.  X  /%•  57*  )  •  ^  <  i^ 

Siv  cUredio  4  ^*    E  punAo  i  agctsr  i#  pa^ 

nlloU  »   &  =3   tpfi  if  iM  )  itertiP  reAi  ^C 

Patet  continub ,  ^  ^  {inum  efl^  angdii  #  C^/» 

^m  dnplus  eft  anguli  dAM  ^j  nam  poftremi 

illius  menr^ra  eft  dimidium  arcu^  4^  \  pno^ 

ris  ^    qu^cp /ormanc  4l»e  radii  4.C«  &  ^i  C 

menYura  eft  totus  arcus  Ad^  ergo  cum  if  M, 

s    f  ^»  eric  i<iM  ut  finos  dupli  anguli,  quem 

Skck  linea  direAienKs*  if  W  com  norizontali 

Jf  Af.    H;  Sie  diredio  A  D ;  erit  eadem  rede' 

Aoi  fi/iuf  anguli  i/Cl^  (  fiam  arcus  quicuo*- 

cue  ntnti)re^iente&  (erpicirculumiaut  angu« 

n  contigui  .H»bent  ^epsdem  finiis  re&os  fifi 

TrigonomitrUm )  •     Atqoi^  ifte  duplu^  eft  atiir 

gtili  DAMi  ergo.     Scilicet :  menfura  an« 

guH  i)if;M^eft  dimiaitirti  krciisifli&f   an* 

^uli  vero  dCN  totus*  arcus  dDlf  :=:   toti  ar-  - 

cuiifiX),  cum  chordie  parallels  in  cirailo, 

aKqu4tes\arcu$  intercipiant  / /rr  C^faeK^rtaei );. 

e/go  Nb  ss   Adi  premaeque  ND  4^  Dd 

z:z  A  D^Dd.     UL  Sit  dentqoe  diredto 

AB  inter  priorei  medta  ;  manireftum  eft  : 

acigulum  ACB  duplo»  efie  anguH  BAmi^ 

pfterii  tere  fiooa  eft  Mdius  ^ta  Am^f^ 

ergot  '\  &hW 


%%6  SiUklti  Oftn^tt 

S€b$t  Ffobf.'!.'  lHtmnlnarf  bcrUoiniJem 
§^imatf$  jdSus  amplttudiuim.  Saluth  :  fia(  /f  tyi  ss 
jiC;  dtRgnablc  rtcM  A  n$  fkctut  ampUtudiQem  maxl» 
mam.  Sun(  «0101  ainplicodinet  in  rfttione'  dietoram 
jgnuuoi  \  itq^*i  r^diuf  eft  -pmnium  finutHii  mtximoi^ 
tinde  (k  fim  totta  dicitori  ergo.  Qvkttc  fi  pttaOttm 
fli^i  firUwbtm  jaetat  nhr'4  m  ,  attingl  non  pottrif* 
Similiter  mH  eKhtbere  ^meft  ihaximam  jectus  hori» 
2omilit  am|^cii<tinem  ;  ^km-m  Bts^A^m  (  p^ 
Gt9$mtrimtot  '&itit  emm  btna  ejusdem  dreufi  tan», 
geniet  ok  «odem  pon^t^  m  doetfr ) ,     j4m  vero  sr 

^C:^  ^  'A^i  fivf  tPmtur  4tfpU  altitudim  iSh 

§d  quam  gtttik  dirtcte  jutfim  eadcm  viilocitati  proje^ 
8nm  afioudatct^  vtltx  fuu^lmtatem  ucfitirtret  ,*^uu 
fryicittir*  . 


ProbUU.  J^Hru^ttfiri  ik^uim,fiik  fua  ahtU 
tytmur  b^rizoutaltt  maximu  jalbtt  au^Umdo.,  .  Solutiot 
tmplitodinet  jactoum  fliot  m  iintif  dopiorudl  angUf^ 
Ibnira  elevationli  machinc  bal)i(lic«  ^  tf,  praf*  )  ; 
ffgo  com  iinof  pmnioiii  maximas  flt  fihos  angu^  j 
rlctt  (  m  90^)1  directio  fiib  tfigoto  45^  dtbic  miP 
iHmtm  tmpiitiidiiiem  jtciiii« 

Probl.'J[IL  Pfmnti^ara  tdtijpmum  fimkt  pn^ 
JfSilii  puuSum^  Solutio  l  ^  jID  Itntt  dirtQtiooit 
(fy.  5  g. )  ;  v^  C  ^  horizpnttlif  amplitu^o  jtctof ,  t 
COjUf  dimidio  0ri§;ator  pefpendicolarif  CF,  dum  oe» 
oorrtt  dttai  linetr  dircctionif,  *  Htrc  eadei|i  ^erpen«"  > ! 
AcoUfb  CF  biftriam  (tcttor ;  functom  interfectto» 
liis  dtbit  titlfimom  ptrabolA^defcrlb^c  ponctom, 
ConrblOO  coim  liquec  iinstm  directionis  d  D  ftrt        : 

Migmim  ptrtbola  ^  iteoiqo^  iineai^  <r  ^  fi^haupm 
Wh    Eft  wrg  (pir  Qtpt^'  mvf )  ^{m;fn«  part»       j 
b^iict  ^Rpb  tWwk .  fivo  tblmdinis  tls  «^g<>* 


Prob), 


( 


4 


fHiiUdhtiim'  itUrndiUKN  r4tionm  umpariifn  /  qnilfm 
ghU  fkmm  ferim*  Spktio  i  Inveniariir'  fifans  cr» 
«olortiiii  ,  quM  fiMRtWt  dct«  cKrectitms^^ciim  pl«n4 
Mntodo*      Dfc»  t  tmpmL  kpfikiini  trtHic  ut  Itnui 

qutbai  14^  p«2^aim  Jf  ^afting^tiir.  Eo^ca>  t^tn* 
Mjfe^  ^uo  globQi  dirtctimie  yfD^  ver^^y^^i  impuU 
uit  ^  ^jdefcrctuf  in  Af ,  decurixrct  rtiotii  cqvabill 
irectaili  ADf  ftljtd^  qnla  (bla  vt  im|rre(!a  itqtiabU 
Jfter  ^inte  accedit  ad  M ;  ftfoindc  t^fnpora  fonc  i4K 
rcctae  k4Di  ^  Ai.  At^ui  hn  (ont  tit  limit  anguk 
lorBin  projectioiiia  D  AM^&t  iAM-f  efgo«  Pr«  nn 
ftectx\#^D,  Ql  Ai  fiux  ehordc  duplonHm  #rcttiio% 
^m  0ietioptur  dictoi  angulos.  Tuoi  vero  omnis  fi» 
ima  reccua  eft  diinidiam  diprddt  «rcoa  dopti  (pn* 
THjpis.)  ;  ergp  cum'  dupta  (iht  ut  (impla,  orunc  TCf 
tttt^ADt  &  Ai  ttt  itiiua  angulorum  projectioms. 
Jam  difflcjle  non  erit  capto  iuiius  jactui  experimentd 
^terminare  tempua  i  qao  globof  quivia  s^fnpendnma 
ptioti^  &  eaditrt  tuliiiiit,  gyri$  qkmttiiMe  ett  «i» 
ieim  tnmbiu^  igipiiUni  ^b  qaam  dircecioiie  plioaf* 
ierieU' 


.\'.\ 


De  mota  ia  ai^cu  drcQll» 

$«  t99.  Si  grtTC  Ittflif  ptitiAreoiificle» 
ratund  rqrpendttur  e  filo  i  aiu  virga  rigtdii 
^  inflexili  ^  Cique  alterum  (ill  ektremunci 
eppendatur  punAe  cuipiam  immobili  ^  iiA>> 
betur  ftnduhm  fin^Jex^  Si  eidem  Yirgs  ri^ 
gidiTi  fc  gratJUtts  etpertt  ippfndikmtr  fhh» 
ra  pendera  i  90«  (imu)  moTeantari  mof a  ite 
loco  fdo  vlfga^  liab<bitur|«ii4MM  iiii^ 

'iWs  >  §iMQ.  ' 


§8S  SilHifUi' Ofat  PB,  ■■ 

1«  80a  In  atroqae  pendolo  aTtffOX  i(r 
|je  hioc».^  illinc  procoruoncs  (  qo^  fioo^ 
fi  filum  .«.loco  (bo .  dioMixo^nir ,  &^  pomiai 
lapfui  Ao  relioqoatiMr  )  aodiam  ^eiUsU9tm » 
guc  vArUUmi^  qa«  ySkifWir  liinr  |  li  eodooi 
tempore  abfoWantar ,  Tel  hmlyfiwckrim^t ,  fl 
bref iffimo ;  iftud  enim  Latinom  ibnane  to^ 
ces  Grarcx.    In  pendtflocooipofito-i^uj  Tir^ 

Sat  pondum »  io   quo  Iji^lati^  c^ter^  j^nr 
•ribii^  locandiim.  o(rot  grave  opicoai »  uc 
iobcioeac^f^fiffiM/mo  fktlfUx  immf^fM  s/ieht^ 

mm  I  Tocamoi  amnm  ^/HUMimii^ 

.-.    •  .  .  .  •  > 

'  Coritl.  6mii€  pendoUm  compbfitom  reiaci  pok 
k#ft  ai  (imptex;  auocirca  'jm  m  ftiidwh  fisfUet^  #«• 
^#1»  fo  cmfofio  tocum  babtatu ,  tfi  mceffe. 

4  ■  d 

ScM\  L  V^Qodcanqoe  pendoium  ofHflet ,  ptt^ 
ilfndrmbveH  W  ^avitaHk  relpettiv^t  \  tiani  vi^rtfi;^ 
fci^  abftltede  mor)(ndQO]  ^effct  liftea^kd  horizontem 
Mrptndteolari.  Idem  efio  jiidiciiim  de  olciUitlonS^ 
Mf  non  jam  ope  fili ,  anc  virgc ,  £ed  m  curvo  canaii , 
fictit,  io^fiMI  ex  ptrre  oppofii^ppft  imnm  fonctom 
babeinir  etifVi  prorAliKicmk/eefimiKf^nort,  & 
fimilitcr  pofita.     Qne re  iftif  epplicari  pottronty  qo«  ad 

|MMb/9i^{f^liacioiifli4^im«^r  ; 


Sclfoh  tt  Qocrff  cnrva  coiifiderari  poteft  tf n- 
^nam  compoiita  ex  infmitlf  Itneoiia '  rectis ,  infinice 
parvif ,  qnie  ejihibcaiit  longitndinef  plaiiOrnm  infinite 
parvonmi  (f^  59  )  «  Hinc  eft|  quod ,  cnm  de  pla* 
^  indmaiii  i|erem  §/•  141.  ^fo^t  koic  loco  rc^ 
Anrnvt  t  qw  ^  B^  \  eeltritatte  ^  ^  fn^^  *• 
Jee^flmm  .pn^t^nc.  |lec  iolicite  notandi  bi;eviter 
coimgiiabo.  Omdb  prope  tbeoAa  pendoiorom  hiiic 
"  •   ^  rcfpe:- 


HfMlllill  «ft«*  VWibd  inmn  pierii((iqulr{p«t?Aiti  jtixin 
kfi^mihmflafii*6teoifntndi  S*,  cclcriratem  =  C,tem« 
fm  ta  T\  gmteatem  refpectiram  =3  K''  ^iMitiam 
irtf»  Jkutidum  Mtndinem  p/«ii/  toftfti^tTim  ss  /;  cc* 
teieitem  m  «1  cempos  s   t,  grartcarcm  abtblutant 


;•  • 


§f  101«  T>if€tnfus  cmrM^is  pir^lsmim  in^ 
Kh$mtm  ift  'unif6fnaiir  Amtitaxui  (  (1  a  fti^io- 
ftei^^tatn  * Inedto refifterite  ,^ pcr  qiidd gfa« 
Via  fbrutitur ',  aUisque  impcdmieAns,  acce]e« 
titronis  abftr^h^tar  )  .  Ndtn  in  quocanqu^ 
punifto  plaiJi  mclihati  conffituatur  corpus  D 
(fig.  13.) ,  femper  ^lum  DGE  idem  erii^ 


pora  VI  gravitat] 

tum  acceieriht  /  fic  prorfus '8b  £6fp'ir&  4i 

Srarltatii  rtp^tmyk  per  plkfodM  rrfcmaturii 
efcendentia«  Scilicet  :  in  delbenfii  bdb 
pUnufn  incljnjitqn^  |d  vjm.gfaritatJf  refpe- 
^ivit «  aiqux  adfeo  \,  immirost^  «  Qvgalu  mm^ 
tnitfius  fit  a0CfffiA,i)ttv«  m^  «lur .  lametfi  A 
plam  fito  impeditt »  itidem  mmor  accretcac» 
iqiiaiii  indefi:enfii  libero,  tamen  fini^per  aii» 
Aa  majorem  cdlferitatetn  rl^petftiTam  towSh 
nentcr  creabit* 

fim$  #e  sOTiiitf ,  ftt^  /.«160:  diSMfimi  ;  fuoelrea 
I*  Spatia  font  ut  ^eadratt  temporam ,  irel  cekritt» 
tnm ;  nam  Si  4  ^  TTt  /  r  a  CC%  ic  (HM.  yi. 
iU  Tempora »  icemqtte  cdirititei  iimi  \m  fitione  (&• 
^uplicsca  &idonua  i  Mm  #^i ;  #fjo  Tt  i^  C^ai^ 

111. 

4 


m0  C;  e  tA  Tt  f»  iV*  St>atimo.4  grftvi  in  ptfM 
incliitato  |>trcar(iini  ^ft  fui)do|^l0(p  illi^i  i  qu^  «m 
dcin  temppre  tboo^em  mobUi  mifkirMter  decufroir 
irecor  tekritMte  fiualL  V.  Gravitas  re^cctiVi  Oft  vg| 
conilanii  oim  &miliW  gtavitasabfbluta  fic  coqiiain 

}mtaum  u0$  fir^fnJiiumri  inira  idtm  tmfut 
genium  I  ut  ^mk  incIinaH ,  dtituJo  nd  lof^tmdl^ 
H€fn  ;  Cve  C  i  i  t^  4 Bi  AC\(j^  if,  )  ^ 
tim,  Celeritotes  fudt  tfii<Sbus  pleiil  Viiriiim 
bcceteratricum  e^antikin ;  tiSttms  Veto  Ieii>» 
per  c&u^  fuii  pro(lortioditi  elTe  debent  | 
^uare  cum  vis  grj^vitotis  refpe&ivx  iit  ta 
irim  gravitatis  abfolutie  ut  AB  ud  AC  (§^ 

i47.)i  ^^>^<tt  celerit4tes  iii  ciidein  ratiosxft 
jl&oporter* 

Jphttiiim  ^  ijMu  9§tUm  Hmpoi^t  m  jfrtt^ifatji^  aijhtkt^ 
^oHfiintfir^  mt  fian»  incUaati  ahihnda^  langhkkmik 
Nam  ficot  ceitritates  ^  fic  fynxvk  eodem  tem|>ore  «om 
fecca  fiint  tffeccoi  virium  ;  tTgOi  Hinc  facUt  traiioi 
^i^tifii  problematttm  ie^otatiMi  t 


Probl.  t  l^aU  aifituiit^  flmii  mlifM 
kar€  ffatikm  fttttuittni  plaHi  Mt^tMlmM  ittumm 
'dnm  toiim  mnparit.  ^  qna  mtiili  tapfu  prpendicnlaH 
tkcufrtrH  datam  altitmUnim»  Solutfit  i  £jc  B  duditnl^ 
perpetldteiriarit  BD  id  AC(jlp  60$)  \  ethibtbtt 
4^0  (piitiefQ  todtm  ttmpdrt  obKqtie  diiificiendttmi 

Cm  naim  w  B  Mniil  iti|iiii  mit  ^tmittahir  ptf« 


B#  mifu  in  mu  ^mH^ 


^K 


ptti&ictxUrii  in  hypothcttofiini ,  ^afttw  H^MTtto  i 

hirfum  r/  ad  /pMtiuni  iodem  tcmfori  dirtcle  SPnfichifit 
dum^U^  flaiil  altiiudf  4d  hugiUtdi9€ii$^  \' ^ 

ftohltU  Dau  ndim  altmdiki  fltmmf^,  ihm^ 

jafH  hHgitiidinem  bab^uiiunt  deUrtHinare  ratimiim  j^ 
iiorum  iu  fiugnlk  pian^'  eodem  temp0re  Confcimtdorutta, 
(^.60«)  <  5^/M ;  Diiflll  ut  ancc  ptrpetidtculiribiii 
ad  datat  ioiigitudines  fict  Imo:  AD  \  AB  "SA  AB% 
^.  iiiio  :  Ad  i  A3  /A  AB  :  A  u  Mitic  ^^ei- 
^D  >4  AC  =:  Ad  M  Ac  (jf4i.tfJc.iK)  ;  pta» 
Irtdc  AO  i  Wrf  is  ^c  4%  v^  C-;  -  h^  c-.  iS;pa<i4  defa^fm 
^ltfuo  decurfafuni  tuterfe  m  JcHgitudines  piaHprum* 

Piohl.  tll«  'DiM  tadem  attHttdhte  ptautrum  ^^ 
i^fam  lougituiiuem  babeUtium  determiuare  fnunum 
tatiouem  vifitim  rff^e^ivarum.  Seluti^  :  Iti  plaiio  \ti» 
cUnaro  ABC  fiW  vis  fefpcflfvki  ftd  «bralatam ,  utABi 
^C  (i,  147.;  .  Rurfum  in  plano  ABe  eft  tit  ASi 
Ac  (  ilid.  )  .  Sctt  ;  (i  gravitas  #b(bluta  VO^ltnr  m 
Vs  relpcaivt  arJ*».  fi«  li«oi  jf^t  /J  ss  AC:  AB. 
lldo  :  r  }  V  I  /^^  .*  yit  ^  crgo  ci^  «*^fi^  pttmtf 
tdto  X  r  t  R  ts^  A  C\  A  c  \  h«  e«  ^f  diverfit  pUuk 
iandfm  attitudinifn  babeuttbue  vires  rejpeltivgt  fuut  rU 
iiproce  ut  plancrum  longitudinet ;  qood  erlt  dctermi» 
tiandom* 

Sebid,  Therorcnift  Mathcitiaticimi  eft  /  Si  fittf^M 
proportlonci  cjusttiodi «  ot  pritntis  conrcqiicfiji  pr^* 
portionls  prlma;  fiat  itl  fecut)da  proportipne  pri^li^ 
enteccdens  |  &  rccundus  antcccdeiria  proportionis  pri# 
111«  fiat  lccundiM  confcquena  proportionis  fecundc » 
liarci  proportioncffl  est  etque  pertnrhat§\  h«e.  MHqfiAl 
terminoi  effe  mifrM  proporcionuiiaii 


It^  if9i^  IT.  C^^t  V!t. 


*  '^  ytoit  ly..  D^  diverfis  ff  slHiudmiim ,  tf 
tongitwlinihui  ^la^rnm  dttfrvliumre  tmidem  fmtumr$ 
Irattoitem  virium  rtJ^eSharum,  ,  Solutic  i  Sinc  pUini 
dtto  ABC^  Aaic  ifig.  60|  &  6t«  )  ^obtiAebicut  de« 

V  n  AB 

IMO H r rises  Ah\  AC;  proind*  A  pi  — '• — -. 

'.••'•  AC"' 

ILrii^s;   ai:  €C  '^  iteruinqae  r  a   *■  *^*  i 

rorrq  cnni  jrqiulia  «d  #qiialia  &cl ,  fieri  debet  i^  lE  4 

J^x  A.B    '    V  >i  ab 
r  s3   -ip.* — -~  I  ■  »     ■     ■  •    Utrinqnc  dividcndo 

AC  '49 

AB       ab 
Iftr  r  33  V  ,  obiitMbls  Rtr  n  ^— •  i  -—  =* 

^B  M  «<»  «^  M  ^C  Sicrepcrict  iiSat  virn 
ifft  inratiaue  canfojlta  ix  din3a  altitudiiOttnf  Vreci* 

^iraca.  lcngitudimm. 

$•  203.  GfOfOi  Jefiifidens  pcr  pUnum  hclU 
Httum  in  fim  ^m  eam  actjuirit  ederitatctH  ^ 
^uam  in  fina  ahiiu^knif  aequifivijfet  lapfu  pcrpen^ 
Jiitdari  $x  aadcm  attituctinc.  Demonfir.  Seu 
£orpos  obitquei  (eu  direde  defcendat  i  dc« 
ilcendic  (emper  motu  uniformtter  accclerato  ; 
proiode  fcmper  C  2:  F  T  (  §.  i6o.  Car,  XL). 
Eaautem  F:R  vz  JC.ABiH^^i^  iteni 
ftmpus  defcenfns  per  altttudtnetn  plani  ,  eft 
ad  rempus  deftenfui  per  longitudinedi  ut 
AB  \^C(  quod  infra  dicam  ) ;  ergo  cele« 
ritasi  quam  grave  acquirit  in  B  defcenden? 
do  p^dBt&^  4C  K  ABi  iterumqucf 

celc- 


.     torod^  t    ^Uatt  g^ivr^  ^Miub  f Ar  i^tf^  «te'/fft; 
^itM  plmnrifm  Utfihn  wftima  ^hriuaM ;  ]pM  *t  ^ta 

^l  L    Dicts  i  Mobib  tjteaendthi  ptH  )4^ 

ditktiuf  fiioVertir,  qUftm  ptr  yf  < ;  ac  promdc  pofitk  tcto 
ipo)r«illt  lh*q^aiirM  Wfcai»  g^AvMtik  f&feim^  wf^ 
ins  Cm  ccDecitftttil  cqtmles  hon  «rttlil,  icd  iMijKMrt 
fcnajfo^i  rcipnodc^t  Mjlcr  ccleri^  ^  1(^31(01»  taiitaiar  |L 
^  cel^ritaccs  cnim  fintMi  orVviki  fiium  ticbcht  iiii|mlfibi|i|| 
gravitati^  omnibui .  infotiX,  fitmptift  ^  xot^jjUt  dcK0i(»l( 
itd^^orc  hAbitis;  It.'  in  plaho  ji  C  rc^ohdcrcit  f^ 
iqQidcHi  iniioA  iehtfori  ftiajbr  telertt)»  nhalis  ,  hi!(l 
^tij^  p9h  cdlcritliir  impcnlii  fii&Icc  ih  ^dr&onVhlr 
jpbrtii^C^  quam  iic'     '    '  ' 


ik  fiit  piafH  uHfinki  f  Oa  ihcC  figkAi.}  UMh^  ^ohMk 
teitrittt»iA  ^ ,  ifffcihi  Mfttirttfit  i^Mdeifsi^  p&  A  '0^. 
Kam  defeehdchdd  per  A  C  acqUittret^^aiidmh  v  V9^^ 
iapra  perpcDdicQ^ri  /^eicAB  {  \,  frt^. )  ;  at^qhi  ,banA 
cahdeih  dbtih^  dctBehdehdb  per  aubtcuiVqUc  j^]ah% 
^Qbd  bitchdb  :  ih  dbf^chfil  i^ler  0  E  «cqUirit  'cahd^nl 
celctitateinj  qiiaih  dadbhdb  Bbt  tf£:!h  EFtotru^  tiha 
deih  i  quam  Cadehdb  htlr  Ef\  dchictUie  t)d*  I^C  itc». 
rtim  cihdcih  j  ^hath  ttdcehdiehdd  jpdr  Fr.  Eft  Vtf^ 
dE^  Ef^  Fc  sg  iV^  -i^f  »i|&i«si:  ^0  r 

^ri^at.  it   §€d  chim  :  hihilhle  beicHtiti  HibbiiS 
Ofiieiaiit  cnguU  JS,  F;  €  ?       jl^.  biliil  cd  fchftM) 

B  b  i  ^ls^ 


s     I 


j^  /r JPfff  s  vimv  %.  iPcUritlteni^  iti  SogvAii  oinre 
panfSs  dttitfltiTi  majortfln  non  «fle  qatntiratf  infini^ 
tcfiimi  Iccuildi  ordiiits ,  qudt  conteitini  poteik 


' '  (Vo/£  Jli.  Qttftvis  Cttrvt!^otlfi4tniri  pdteft  OH 
^mppitta  ex  iufinitis  planis  inclliMttiU  ;  qua^e  tnobiid 
pet:  cur^iini  continuatn  defcendcndo  ex  Ain  Ci  .^^ 
obtinebtt  velocitatem  ^  quam  obtinoiiTet  de&tndendo 

,,  ^  ab4.^  r4MJtw  Mfien^  p0tAC  hB^tuM^ 
m»ilnaHi  incknMM  efi  Md  umpus  d$fc$njm  pn^ 
A 4  dtimSmm  yuukm  pkmi y  utACiABi 
§ft  T:  t  ::^  S  i  f  s^  ACtAM.  Dcm^ 
ptdtenCui  ctarporis  in  prl^o  indiMto  e(l 
i)hif6irmitef  icceleratui  ;  1un«  T  1 1  U  zi 
4C:  AB  ,C§,|.<0)).  TmAJi  (te.<oO 
eodem  tJKmpore  decurrituf ,  quo  il  jB  bpfil 
perpendicuhiri  ($•  16S.  ProiA  /•)  $  i"^^  ^' 
14  s4  if  Ct  4J0l|  tatix  y$nto  A  C ^  AB%  AD 
ttes  GonttfHlo  priKptfrrlottJkl  (  h«e.  AC%  AB 
a  'i<JBt  ifi^  fM.)j  proiiHle ifCi  /  ifjSt  =9 
AC i  A  D.  Vel  ideo  racio  ^ltera  aiten  fub* 
Itittri  poreft}  (itbftituriocie  Tada  obtineblrur 
TTi  tt  zs  AC^  t  ABt  ^  &c  utrtnqiio  radt« 
C«m  extrahendo  Tt  i  ;=:  AC^  AB^, 

,  S^l  Di:4l :  (t  fuerint  tr^  continue  prdportio» 
mkt^  e.c.  #«  b^  ^i  obttniri  hanc  pcpporlionem  « 
da  t  tft  :^  at  c*  Si  enitti  a.'  i  :=:  h:  c\  btbetbr 
ac  ^  bb.  Pada  «qualU  per  eandetti  quatititfltctn 
l|  imiltipiicando  obtinebatiir  auc  ^  ahb\  denique 
&ly«do in profortieinetn  ittaai  bb  ^  a\c*. 

Cor$t. 


-j 


Oirir.  L  Si  pliira  e)atd^>fMtd3intt''pliibt  dil& 
tniltf  «onrerantor,  rfmpar»  del!99i<us«nl|iK  didlA^^t 
planonim  longitfidin«s«  .  .-y  -^^ 


•  V  t  *  f  •  *     *  t    \ 


CorolL  Ih  tmpoTfk '  delcenttt  'per  f gtifihitii 
qudrumvis  fimtlium  ,  Q^  ad  boriz&iifem^  i!milfte^*ihr 
*clinat>rum  perimecros  fiint  in  r^iioiie  (ubdiipli^tt 
'quornmWs  latcruni  homologorqmt  Cum  cn|a|  iii 
mocu  uniformiter  accelerato  T  s  t  ss  l^  S  l  -  ^ $ 
t§.  f6o.  CoroU.  VllAy  crit.(  r«  fig.  «o.  &6i.)  T;  t 
r=  i^ACi  f^ac  ;  cumque  AC :  «  c  ss  AS  f  a  t 
:=:   BC:  *  c,  flct  dcnop   T;  #  a   /"  W9;l^t*il| 

Cdr^^l!^*  III.  Slmtlct  eifcoIorQm  arcus  (unt  plalii 
initiiicft  fimilster  inctinara »  qaare  id^m  mobile  lid^Qf* 
TQt  arcns  fimilet  temporibus ,  quat  finc  in  ratione  (iib* 
dupjicara  horum  grcuum ,  aot  radforum  iplii  p«>{|Oir^ 

iionaiium* 

§.  20  y,  Tcmpus  dtfanfus  vn"  quAsvis  eher^ 
4as  drculi ,  cujus  Mamctcr  fii  ad  torizontcm  pci^m 
fcndieularis ,  ^c^udtur  tcmpori  dcficnfus  pcr  ipfam 
diamctrum.  Defcendat  enim  mobile  pcr  Ad 
IfiS'  ^3*  )»  dcterminabtr  perpcndicularis  J5X7 
(  nam  angulus  A  C  B  \t\  femlcirculo  redu^ 
cift)  fpatium  codem  tempore  oblique  decur*' 
rendum ;  eritque  tempus  per  AC  7:^  tempo^ 
ri  per  4li?  (  §.  202.  PrM.  /O  •  H.  ob  paral- 
kUs  AC,  8c  5D  itid^rm  anguhis  CBD  rcAa$ 
c(t;  proindeqne  DB  perpendiguUris  ad  CB 
rurfum  determinabit  (pctium  codem  tcmpov, 
re dccurrendum ,  quo  CD  :=:ABi  ergOt 


;t:  t^MEi  TtHiyaM  defeen(tif  ^er  fBumk  ciratfi 
«iiMaAii  Umr  ft  #9111111«  i  «9iAnt«r  mim  Hmpmci 
df (c^nfiu  pe t  ^iiiQotroai^  Cm  W9tsk  i  «iffiiioc^  i 
frqnAri  fiiniliter  temport.  deicenfvt  per  qnosvit  muil- 
vrjffipf^M  ^fm%.\vii  pra  ctior^is  tMWi  poffinij 

r«ai^4fcn«niinmi  cbor4i&  qvtidm  Cm  fim  ton^tih 
r in^  P%rff  Cmt  ^  tt  noh  politionf  t  icu  p«QdoVo«il 
fa^HorizpAtfai  inclioA^iQOf  i^  «  q^^  pfii4«r  ^rfviQi 

» 

)f$^  2Q6t   (rftf^  ihfanJw  /rr  /Ammi  I^ rll« 

^ind4r$  M4fi  i  nam  celcrhas »  qiuiP  mobUfi 

in  fine  plant  incUnari  conrcquituri  noo  con« 

.  lifiuo  peric »  M  ti  inerci^^  conferYitur ;  or% 

^i^  niQDile  concepto  impecu  ad  candeoi  paf» 

•  tis    eppofit^   aliitudtnem    metu   retardero 

efijenoece  poteft ,  fi  ira  dir«^  ferat  j  0^  e« 

corpui  ^K  4  Updim  five  in  C,  five  in  #  ,  ah 

fcend^r?  pQt^n  ad  aititudincm  C$ ,  vel  C  n^ 

\iAi  tempora.  afcenfus  rcfpondehunt  rempcH 

*Viqm$  (jefccnrui  p«r  pl4na/«ti/air  tnclinau« 

SckoK  Si  metuU  defeendcns  vi  grsvit«lit  (^tu 
(jjnni  eao4cn)  »  sot  ptr^llelsm  dire^iopeoi  perp^nvi 
iirgearur,  «eceleratqr  niorvis;  oianet  enim  celerirti 
acq»tf?ta  ,  fi(  nova  eonfpiranti  continoQ  t^ditur  ) 
cnmque  grtvirts  in  vidnti^  noitpfs  confttntivt ,  mo- 
biiQ  squtlihtts  temporibut  «qualit  tccipft  celeritttit 
inercfii^ntt »  aileoqnQ  motns  uniformiter  tccelcratuf, 
fit.  fi  gr^vitas  in  eorpus  jam  moruro  pcrpetuo  tga^- 
con^rvia  dirc^ionc  ,  cpqMaU)>«s  tcmporihus  9pqu||li« 
^nt  cc^Ti^ati$  cieorcmenta  y  motusqpc  uniformiter 
1  Cfardahirur ,  non  ante  cKftinguendus ,  nffi  cntn  ino» 

Wlc  pcrvcncrii  ad  c«m  alritudincro  ,  cx|  qoa  ^it 

CVHlt 


redica  corporit  nutlibas  tcni{^ribus  cqualci  cctci^ 
Mcit  gradus  gcncrcr,  &  cxftinguat ,  dcbet  in  D,  (k 
r,  M,  dcji  ,  cliisqitc  ptttiAis  ffmilitcr  pofiris  idcai 
cclcricatis  gradus  invcniri.  Jam  ad  piudtiU  g(««Uiill 
,  guorum  rheofia  manifcAe  dcrivatQr  cx 


§.  S07«  Si  jnnduhm  $x  punSh  '^mnis  B 
hp$tur  inC  ifij^.  6^.\  fin  nUSlum d^fimdi^  m^ 
tu  uHtformiar  scccliraio^  Cf  in  B  4Cfuirit  cmk 
^lcrii4$tim  »  ^m.  mMi  ftur^M  4fc$ndirc  fofft 
in  J).  Cum  cnim  qairis /pi4u|.vis  cprvx  afr 
cus  coniidorari  po^t  ranquaiv  comppucaf 
ex  intinicis  planis  inclinatis»  in6nit«  p^na» 
poterunc  cuivis  arcui  accMifnHHiari ,  ,quse^d# 
ono,  auc  pluribiis  plafiis  indiaaiii  di^a  jT^iKI 
•t^ui;  ergo,  v 


C  208*  Olcritat  per  ^ucmvii  circutt  jrflMi 
CB  (6f.  65. )  in  B  acqmfiis  $fi  sd  Hi^tim^ 
gus  Upju  pcrpindiculm  pcr  totgm  diamctrwff  AM 
saftiiriraur  ,  ui  cbcrdu  CB  ud  diimnrum  A  Bi 
Ducacur  enim  C  m  perpendicularis  ad  A^4 
eric  celeritas  acquifira  per  arcum  CB  h:  c$h 
leritaci  acqulficae  per  mB  (S^aoj.  CcaO^.Ji 
cumque  celeritas  per  m  B  fit  ad  ceieritacem 
V€f  d  B  uc  r  m  B  ad  f  AB  (  h.  e.  in  ra« 
tiooe  fubduplicata  fpaciorum  $«  ifo.  OroU^ 
yih)  eciam  celcriras  per  C B  efle  dcbec  a4 
eeleritacem  per  if  £  uc  r  tt$  B  zd  r  A  B^ 
Elt  vero  ^ium  ACB  ^  Cm  B  ^  adeoqun 
ABt  CBz:-  CB;  mB^  proinde  AB2  ?  CB% 
:::AB.mB  {§.204.  Sckol.)^  S^CBi 4 B:;:::  t 

Bb  4  •       inJBi 


%Bi  't  ^^»    'Qi^oniam  itgo  celerira«  per 
fB^^  a4 celcritateim  [>tv  AB  nt  ^  mB  ji4 

f  '  Or^ff*  Si  celaritaret  pcr  plures  e}usdein  circoU 
jlM^caa  in  potido  infino^  A  aeqjii^t^^invkem  cd^ftpraa« 
W ».  Qcmo  non  yider  fore  easdem  tntbr  fa  ut.  fiint 
liorain  krcaom  cbord«  CA,  <&  £i7. 

f •  409»  'Tmfor^  ikfirilfuf  pn^JtmiUi  du^ 
rtm  iiriuhrum  sitw  CJBO,  ^ifg  (Jli*  ^^) 

funt  in  r4iigff$  Jbhdupticat^  hrum  arcuum;  ^  SY* 
ftMcttfAtti  arcuifunr  plana  infinita  (titlilicef 

SQ^mx^l  tfijU)  tiid  decurruntur  rempori* 
k^  ^UM  Shf  irr  ratfone^  fut>duplic:ita  fpa* 
fiorum»  (eu  longitudinum  ($«804«C«r,i/i)| 
f rgo  cfiaro  arcu^t 

}trtm*fiim  90  rw^nf  fiihJ^flkmf^  radhrumi  Aine  eiitivi 
ipciii  imilca  m  ra4ii ,  id:  eft  ut  IqngitucKnes  lieaini 
M|i4^1orum  \  qviar»  ii  radii  dieanrvr  L  ^  &  /  v  ^^ 
Xff  t$  .s,  i  ;/;  &  IJ:  /  p:  f^i;  //.  Hinc  jain 

diffiyile  non  erir  datis  tripua  bornm  terminorum  iHf 
tiitire  quartunn  \ 

'  '€.  ftfO.  JfuMcri  offiillatiBnHm  ^penJHlit^* 
V^fk  iongitu4inis  ^odem  aliijuo  tcfnpon  corlfcS^ 
tum  funt  in  rationc  rccipn^a  fubdupHcata  Uniitt^ 
^num:  nam  fimt  nurhert  ofcillaitomim  rtci« 

Sroce  «t  tempop^,  qu^e  funcin  ratione  fiib* 
rplicata  longitud1num(§,^r^f.C5ir,)/  ergd 


P#  mtu  h  srm  tirmHi,         yj^ 

ScM,  Kurtitroi  ofcflUuofium  t^  Inmfl^  <if 
teftipori  cx  eo  conficifiir  ,  qtiod  otcillauQnutn  ramc^ 
rus  efTf  dohcat  co  minor  ,  qiio  m^jus  tf  mput  fingoiit 
picilUribnibos  pcragfn^is  impendt  dfbet.-  Iternm  d^ 
tis  (ribut  terminls  fm\t  d^terminabieuf  urriuttibrt 
j^nciiili  (ire  longitudo ,  icu  nqmcrm  o&UUtionum. 

$t  3 11«  Jn  ifiehroHh  divirfifwn  fenduiH 
rum  0fiilla$iontbu$    vir$$   grgvitmif   mekmticii 

Junt  ui  panJuhnim  longtt^dims ;  fiint  enim  yu 
re$  conftanrcs  (  quttef  habentur  in  exigui| 
ab  «ad«m  fupergae  terr«  diftamiis)  propor^ 
ti6n«tar  fpatiis  eodeni  tempore^  defcriptis 
(  $#  8oa«  CorBll. )  ;  fpaciji  ofciliatiooibiii  i(b« 
chronis  confoA^  funt  arcus  iimile$^  live  «i^ 
cobt^  fimiiibus  proporrioMles  radii  ,*  radii 
funt  iongftqdinei  pt ndulomm }  trgov 

tminlum^  art(  ftnduh  ffutdem  longitudittii^  If  itqtnh 
Us  mui  demrmtiis  ifichrQM  effi  dshnti  »oli«c  cnmj 

bypothf G S;  $m  Ttt. 

Coratt^  17,  Erg9  ft  idvn  pendulum ,  Wf  ejusdtvH 
hffgMftsU  penduh  in  vari/f  UrrdS  hcif  ifocbrm($  non 
ffnt ,  vis  gravitatig  conflans  mn  efl,  Ubi  plurcs  hsJ 
PCntur  ej^sdoin  penduli  o(eiilarioncs,  vis  grwtatis  ms» 
jor  cft  ?  olii  psuciorwi  minor  cft,  Hinc  f  i6i.  Jfi 
finJF.  docui,  m^jovein  graviCMcin  cflTc  ySfii  po/¥  tcr^ 
U,  qaam  Jkh  /EqHaten.  * 

.  ScM.  /,  Monul,  moncoqne  itorvm  i  qn*  btu 
ftp»Wl  ad  pendulorum  hiftoriain  fcripfi^  ftripfi  TOcm 
rcm  sh^rahendo  ab  adjondis ,  e,  c.  Ai9im  ^^  « 

Bb}  •        ir^# 


nnUa  haber^ntur. ,  pend^li.iiiotiis  foret  perpcnmf  ^ 
j^  omuioo  exa^liflimuSr.  Interea  rero  propter  mcd^ 
l^ffiflcinum  ,  fri£^ion^m.  &c,  I  (iicceflive  miaoQCitw 
^iciUMioneii  dpnec  fehiini  pendiilani  in  B  conq«ie£i:flt; 

SeiaL  iL  Ad  ofcillationes  i^endQlornm  tevoe^ 
fhmrnw  elaflicamm  aghationes  ^  de  quibof  p«QC«, 
.fnt\5lli^o  «utedi  nomino  fibr«  eltftic»  chordm  tenaiC 
6memf*'JIB-*\fif,'46,'^^  «qutbileni,  &  (otttmetaUi* 
$4mj  qwt^  tmi»  m^gn^m,ft0d9^t  eUfticititem  ,  fiibtiv 
de  vero^nimis  tfin(z  eandcm  psrdat.  Ejusmodt  libri^ 
^ii  fiijmeiitis  tfnuiinmis  iptcr  fe  conjugitis  coneipi» 
mus  CQnftarc  qmpi9  corpora  finfticn; 

W 

\U  SV  1iht9  alicujot  fidrfma  //,  &  £  figantor^ 
svedtoque  ejus  punAo  C  appendator  pondof^  iB£Af tnt 
thorda ,  6l  abibit  in  fimm  jiDB.  Tom  fi  fluird« 
tcnf^  qoidfnf ,  (td  nonduoi  inftcM  medinm  pmidniii 
C  iungatur  cum  mcdio  ejusdem  diords^  poftee  flexs 
tundo  P ,  r^£b|  C  D  fe  pundt  CQnnede ns  dicitof 
o^itta»  Si  dentquf  centro  $ ,  rf  dio  B  C  de (criba mr 
orcuf  C#y  fa(hibet  De  qaantttatcm  ,  qoa  dimidlA 
chordf^  BCy  pcr  fiii  inilexionfm  produ£^a  fuit.  Or* 
4o  jam  po(cit  eximinafe  rf tionem  ,  qoam  ed  inviceiii 
^iconi  v^  f&erfiam  temkuf  x;^   t  ^  vis  e$ttdm  ivfieBtm 

X»  i ,  figitt4  /9  C  ;s  $  i  f9ffgffu4Q  cbgrda  nondeip  ini 

IU«   Pnfifi  figink  $4m4um    ex^  tdktw 

l 

fr%fnrth\lx  tzti  n-^l    Slvf :  Bft  vis  iufleSent  $4 

frim  t^nffmk  (  anff  infiexionffii  )  ,  f#;.  dttpbt  figitta  ai 
dimiii^m  ^h^rdgm*  Vis  tn\m  mere  tendens  exhibetoK 
f ff  rf df m  eh  i  quare  cum  pdiitf  figltta  admodoin 

u:%n  &rfa  ^^sV^i  ctif m  vto  tc  ndois  exbiher} 

jeiffl 


gr^tQino  ^cfigiwi  fMA  pcr  4iagojiuliciii  m  %  $4 

Q«iil  fiiaain  «icdion«i  cpqnclc  liidq  oHrcoimMi»  hi» 

.1-1  '.,    -^ 

kctiif  a  if  =:  -*-— i  proiiiic  411  ai  </^    U»  Ui» 

Cpiiq«e  motentQr  f is  tcn^ens ,  dc  inAcftcnt »  «ffd|^ 
Jfrvim  tafukm  rAtiomtin  ,  fempcf  filgittf  exi^4  c)Qiii 
dem  atieujus  cbordc  CMndut  csdcnit  Viribos  eniq| 
irs  imnKitatis ,  ut  $mmn  $i$muau$  in  eadem  ratioM , 
Dportcf  man^ntc  cadem  longitodine  cbord^  manfct 

s 
cafdem  figimt,  fccQC noQ hahebitQr  i:t:m  a  A'  "^  h 

J/J.  Si  Gonfcranfar  duc  cfaord^  M^nt  iongC|  &  ir« 
^Qaliter  tengr ,  ernntfigittc  minioic  in  rationc  vt« 
rium  iniie^encium.  Semper  enim  ^  $  $  ^  i  f%^ 
fupra.  Quarc  coliatis  dQabus  f)bria  erit  IL  t  i  l  ^ 
4.VT:  4^#  rs  STt  st.  Cumquc  e^  Aypo|/(.  Tsi» 
^  Lss  /i  ent  1 :  i  ?s  5:  #.  Theorema  iftod  ctiaiii  pci^ 
tinet  ac)  vhpi;das  incqQalis  diametri.  IFt  Si  divcrfig 
l(iin|itudinis  fibrx ,  tamcn  dtqualitcr  tenfar  inviecm 
conferanrup,  eront  (agittc  in  ratione  compofita  virinm 
infleAenrium, & longitudinum.  Kempo  e(k  IJL  :  i| 
ic  «S*  T;  /  ^;  crgo  fi  T  =3  ^,  habetur 1 1< ^ i / i;s  i*:*! 
Si  pra^Hrca  £  a;  /,  cficdcbct  I;  1  :«  £t  ^     H#C|  4| 

alia  manifeita  lunt, 

IV.  Cborda  AB  utcunqna  ttf^^ft  hipH$%jN^ 

<b  tamfu^  fibi  rtUa^  ofiillah    Nam  vi  clafticicaiii  fm 

rodit  ad  iitum  priqrem  ;     reditqQC  matQ  ftmpcr  10» 
eelerato  ( (eu,  qnod  via  claftica  non .  fcCQS  itgttC  $Wk 

XH  igct  pcrpctQQ  i  fcQ  f Qod  oovA  cctoiM  kUniUMi 


Cm^isrtrinert j>0tlVr)}  obdfi^  igitiir  innKtimite  cev 
nnreffi^iil  C,  '«hdc  ftj^t. nlM-iori  ^xc9r(iiH9e ,  19 
piagtm  oppoiicatA  irc  ,  iterumque  urgento  eUfttcicncc 
ikwi^dw  oporrcbit.^  %  •  i     .    .  - 

■     ■  r 

tujuf  condilto  non  memini ,  cunnl  ejns  appUc^tio  «4 
Hmirki  ]m'  ftre  atKiqti#(a  (it  ( teile  P,  HiAik^  >  ,  & 
oicillationei  in  exiguis  arcttbus  ciroali  jG^tis  i(bchrou# 
4<^rth«ildarK«r/ 

'     ,     Caput  VIII. 

De  motu,&  prefllone  fluidof  uml 

Dc  prcOionc. 

f.  aij.  F/«/ii  dixi ,  quac  impreflionl 
tuivis  levilfinias  facite  ced(int«  ^  Proritfljma^ 
yiiaf  cedionis  ratio  (tifSciens  efl:  in  particqla- 
riim  cobasfiont  tam  exigw  ^  ut  £ictle,ab  inv 
iMCfim  feparari  poffint» 

ConU*  h  81  pare^a  fiutdum  componentci  facilit 
tno  ffparantur  I  pot^d  alift  fluidi  portio  in  ifiam ,  alii 
to  iilam  plagam  mover!  9  quin  tota  fimui  mafla  in 
liiMidim  plagam  ab«ar,    Comrarium  obtinet  in  (blidifr 

Or»0,  H,  Si  geminx  e)usdcm  fluidi  portioncf 
in  d{vdr(as  pUgas  abire  poHint ,  pprcrit  qufltlibct  flai* 
«11  parr  dSftin^an)  aliqqam  fundi  portionem  preincrci 
^fiftin  fo0i  iimul  nialfa  eandcm  va(is  portionem  pre^ 
tl^Ht  Qotre  qn^vis  fluidi  ]>artio  ,  indepcndenter  ab 
elia  I  CK^rm  poterit  vim  prem^ndi  fundum  vilis,  vd 
iNel  I  4|«o  ceiuinocurt    Ri^ruf  ^  opppGcum  habctar  m 

6Ii- 


ftentit*    •••  M   ..•'.*   t.*  .•;  *   >  r**  •  • 

.C^rdlLlII^  Si  Aaidcirtitn  pArtM  ^Viflime  cObiN 
tetiti  tftti^uc  impreinffni  ficiLe  ci^unt.i  €i  ftciU  tno« 
vctitur,  oportec  easdetfi  «^lutrim)  l^irig^tM»  6v  ^d» 
inodmr  fubtUes  eflcLi}  iSMI  firmiMr  c^renti*^  .frif 
alo  y  iift  i|iag[«i]tuda  ttomd^  lmpc4ii»it  Stibtilitai 
parfioukmtii  itiinUcfit  deduettur  ejc.c^^  4{tiod  fiuid4 
&  ie  k.  aiigofitirimi  eot|»orom  imerviilo  tafititielU  | 
hitic  fo^^c  itiflalitQf  cortMirai.ic  intMiefcntii. 

§.  1194  Flbida  vtl  Umffnm  fiifiti  ttl 
i^rrrag«^r4^  batnogtiieairoci»!  qwrejmdomt 
hecerogenci «  qus  diverfae'  fiwt  deHfitAtif*    * 

JuHi.  ExperitDur  Aije  Vis  qubcon^flMidd  pt^ 
tiuni  j^favtus  ciTei  qttatn  vacuutri»  ific  mdf 
li^uUd  mnU  ffi^  fum  fpMM  iHUgrd  m^s^ 
/id  f^  finguU  Mfmdmm  m^mlsgrmm  fmH.  % 
nam  gravlcas  tmiui  teaflk  orituf  a  gtavitatt 
finguiarum  partinm*  ^ 

$1  215.  l^uids  vmnis  fnmunt  Mrptf^ 
pt  JiMida ,  ^buf  iuiumiunU  Mam  graYJa 
cum  finc,  urgencur*  ac  tendunc  deorfum  ) 
atque  adeo  vi  gr«vitatU  premuoc  corpora  fi« 
bl  rubjeaai  feu  jMirig#ifra  fint|  £vo  hm^ff^ 
m4$  Qtiafe  &  randus  vafis  premitor  a  fioi* 
do  I  &  cjuatvis  inferior  fluidl  portio  i  fbp«N 

fiorei  fibi  Incumbentt* 

"■•'-'        •  ■  •  ■  '       • 


fft        imn  effmi^tfii 


talitt,  i/A  em  tdmjMrdit  Bcnih^  «^ui^  tcfknm  nM^ 
k  pttff^odam  Vi  t  ptiUXi  ittolli  ^  iqiiaindia  itiht 
«qutm  Vtrfttlir  (  tt^  cafen  in  tiftdn  tkiit  ^  ptrdpi  c^a» 
AtMi  t^^ndas  pfx>  tqntntitltt  Ihlllk  ftult  tokiteitff^  «Itr* 
AiiHtfcM  ijluidtt  U  io^Jfi^H^  tf^fjfikwm  mm\gh^ 
Hfi}^  h$  t.  Mll  liiti  de^mimi  ^Q^  pohdtre  Gid  prc» 
tMre  Mttfirftlti  HM  fhbjeaui^  VJMm  toceiii  plr^fHm 
Htl»  dYtMbttiar  >  th  ^  ««{lAk  MBf  tilehtnt  Ipeatial^rt^ 

Vifttt  fptdSei }'.      labrnfn  rttKilief  WelteiQ  pnl&i^ 
pti«s  &ntenHtt  nrti^^  4)n«  jiin  lltcentidmni  oiBtniii!i& 
nis  eft ,  Vtiitltcin  -  confirmttnm  et  t    L  Qnpcnnqnt     , 
Kitco  ci^nfifitnt  liqnidt  pohdnt  (boni  habent ,  &  grtvr-    1 
teietH;  pMiiidt  tjnotnllqte  iot^  ebhlilltnc  >  iiirgehtQlr 
dotrftm^  tqgtopremnnc.     IL  Onmt;ctrpu»  niritu^ 

(td  eentrolll,(|ii||t,v  *  qi>0  ^^  i  j^^'"^  ^  fiuida^ 
Utv  Fiuiclt  hittikhtut  td  cehtrum  faum  ,  ijutrodia 
ISmt  ffl,/^t  nen  pnprtpi  iguidni  {>trifer  hictntUr  ^ 
(hun  innt  in  frofrio.  Stnt  ihlocc)  bon  j^rbprit  coiv^ 
tttartt  hitiintlt^  dtlirluih ,  ^ttit  fih^ulip  Rtlidordnrth(r« 
Itatile  grtver  lliht ',  itqhi  liMipel'  gttVlrs  runt  -,  ^Um 
Mhqiit  loct  teivfifbnt  'Hdldt ;  •trgo;  IV.  Rem  evin^ 
fculit  txpceimeimr  4k  obftnrttiMet  quotiditnit ;  Mer» 
tnrint  eni|h  th  inbt  iTori^ieeUitni»  #(ccndtt)  tc  deftens' 
dit ;  hon  tucem  tifcenderet,  htfi  ter  |)remeret.'  tdo  i 
Sittiilittr  ih  tiibil  cthihiuhicttitiWs  ^ttolVitur  Vtitt^ 
|riat  tb  tqilt ,  oleo»  fluidisnoe  tliit  Ifiecifice  ieviori- 
vllt  i  nifi  Verb  tqtt^  dleufn  &c.  gttVlttr^nt,  neUtiqutnl 
iltt)nefettih  |tib :  St  TfhitH  ciVa  >  hd  in  tbbulli  db^ 
iohgitm  dt0neh§  itre  eVtcnetli^ , '  ec  t^uc  ihiihetgi: 
tm^,  tlcctldit  tqtt}  itoi^ttlh  ttnHi  afceilfionls  t(t  pte^ 
fto  tfrit  iqu^  inctttibcntitk  *  *4tl>  i  JMt jus  tlft  potirdai 
^tie  tnHtRr  I  ^tn  hth  ihlii^#  j   etgo  itr  grtvicah 

E»  I  Vtt  Vteyiii^  iquitimlherrmh  {yiondtrethr ;   tunl 
tti  tqiit  tepiethitt^     beprehchdetur  jpohdus  tlhtH' 

■Mftti  j  ftitntnm  ipf ciidiif  oihhiS|  quit  m  idiA|^)tt 


V 

\ 


iurfum  €/i  ad  Jpdiiuifi  todem  $cmfi>ri  dincle  ^^nfiOgf^ 
guM^u$  flmi  dltiitidf  4d  hngiuidiutmk 


/sf^  hfigitiuiiuem  babeniium  dtUrtHinart  rithMm  j^ 
iiorMs  iu  fingiM  phnp»-  todem  ump^rt  CoijficHmdorUHi, 
(i%'^0 «  •S^^''^  •  OttAii  Ut  inte  ptrpcndicnlaribiii 
nd  dtcal  (oligitudines  iiet  ImO!  ^D  :  ^B  ^  AB% 
4i£.  Uda  t  4di  AB  :=i  AB  i  A  t,  HtHC  m»: 
rf^D  X  AC  =:  ^^  M  /^c  (jr*i*tfx.iK)  ;  pro« 
iitde  j((^ii> :  ^^  ^  y^p// v^  C^.Ke^  «Sjpati^  defa^/k 
^ltfuo  dtturfafuni  iuterfe  m  JoHgitudinei  plan$rum% 

9 

Prohi.  IIU   'Viki  ^idem^  atiftHiim  pta$mrum  'iR 
t^fkm  iofigitttdhtem    babemium    detertnihart   fnutu 
^aiioum  vifHiim'¥^^'t^ivarufH.    Hhlutii  :  In  piaito 
clinaro  yfS^Hrtltvisfcfpe^lfVkadalrroiatim,  xxtli 
^C  {i.  147*)  .     Rurium  in  phMABt  cft  tit^^ 
Ac  (  illd,  )  •     Sctt  ;  ii  gravitit  a!>(blurfl  vo^fttir  aa 

(^»  re(pcdiyi>^.rRt»  &i  ^m^  VK^  «  ^C*  -^A 
Itdo  •  r  \  fi  t  AB  t  Ati  ttgo^ett  ^qua  pgttt^f 
tato  :  >  f  K  ss  A  Ct  A  c  \  h«  |;  /#<'  ^/itfr/Ti  ptanif 
iaftdtm  attitudiftem  halentibus  tiret  re^6tin4tfuui  iri* 
ifproct  ut  plinof^tiM  Uttgitudintf  $  '  qood  crit  dctcritiK 
nandaiti* 


j «  fi 


5fiW»  Tb^orfnaaMathcinati^tMtscft/ SifinfrfM 
proporUonci  cjusniodi,  trt  prtmoi  tonfc^qtiieiii  pii^ 
|K)rtionii  pf ima:  fiat  in  (ccunda  firoporripnf  <{Nf ifiyf 
inttccdcnsi  &iccbndiif  amcccdfitiij»ropprtlonii  pi:i# 
m*  iiat  lecunddi  confcqueni  profjortionis  fcctffi4f|  ^ 
Itaict  proportioncm  tx  etfttc  ptrtartata  ^  ih«f.''Mi^[Mf 

Iffinttioi  f flf  rHtt^Hi  pr oporciofialcii' 

« 

B*  Prttbi. 


|i«        s^  n,  ot^  m 


»ii'     i. 


JProR  ly.  0#t*  diverfi  \S  Mkimiimhm  ,  (< 
tofighmHuiiui  fla^rim  iktenriiumrf  umdem  fmnfMm 
)rani^m  virium  "rtJ^tSivQrum.  .  Soiutio  t  Sinc  pljini 
4tio  >f SC|  &  tf  ^c  (fig,  60|  Oc  6t.  )  .obtinebicuf  de« 

Mo^  r  r;ae  ^Bi  AC;'  pro&idt  H  ai  — ^ 

-»     •   •    *  jf%^^' 

IL  ri  i^  a  «^;  «^  j  tteroinqM  r  a   *  ■■»    i 

rorrp  cnin  orqtiftlta  «d  i^qaalift  &cl ,  6cri  diebet  i^Rt 

V  y^  A.B    '     V  >k  ab 

w  s9    ■II  s  t  %    !■     I  •    Utrinqoc  dividcndo 

WC  -   cf 

-**£       c* 
gcr  r  as  V  I  oktiiiAls  Ktr  n  ^—  ;  -—  =* 

JfB  M  Mnt  0i  M  <^C  Sicrcpcrict  i/A«  v/r«/ 
iA  tHtMimte  cmtf^jSta  ex. dir§3i€ akttudittktttf  V recu 
fi^Jefigitudimum. 

t  -  ■  • 

$i  so).  Girji^#  Jefiendms  ptr  pUnum  tncU^ 
Mim  in  fim  pUfA  esitt  McquMt  ttierimctH^ 
djtiStn  in  finc  sliiitidinie  ac^ptijvifet  Uffu  pcrpen* 
Jiitdm  4X  jesdtm  ^tlitudittc.  Demottfir.  Seu 
£orpoi  obiique,  (eo  direAe  defcetidat  i  de« 
&endte  iemper  motu  utiiformiter  cccclerato  ; 
proiode  femper  C  is:  VT  (§.  i6o.  Cor*X/.). 
Eaautem  r:Rtz  if  C :  i<  4  ( 147  )  $^  itefii 
Mmpus  de(cenfhs  per  dltftudmem  plani ,  eft 
atd  tempus  defcennis  per  longitudinem  ut 
J^B  \  A  C  (  quod  infra  dicam  ) }  ergo  ceie« 
ritas  I  'qiiam'  graye  acquirir  in  M  delcenden? 
do  ptfiliSeft  ;;;  4C  ><  AMi  iterurnqucf 

•   *  cele- 


.  c 


,t»r»iLt    0uriri  gHmHt  mti*  *»  Uitttt  «j 
«ilM.  ^b^itU^^  tk  pilm&  iitaui^  vA"»  Htdfaktir  M 
.fim  plmttrtm  irMilbM  «cfuSmttt  ^dtrittMi  jpMkiE^&ir 


dttlHui  aioverdr,  qUiin  jptr^^;  j^  jproifldc  j^ittii  ItfSrn^ 
i[)«im(ll\ltotq^itflfl««  ^ffcai»  gfivlvAlik  f&p^  ''wfpitKm 
H»  V  A»  cc&rtnnn  «qinilcs  hoti  ttatik>  led  l^ilifNicl 
Itii^^  rc^Qoilclitt  Mjdr  cdeti^  i  «iiiM  'mim  }L 
^  "^  cclcrfritcs  vniin  fincHil  «Hrhiiii  fiinm  litbcnt  ><!i($Uibtt|| 
jpravitatik  omnibkiB  ^^V)i.  i^ptic  ^  tmjpjitit  dcfttfii^ 
c(rt^]porc  ti4brtis;        jj^.  in  pUhO  ^  u  rc&ondcm  ^ 

Snidclb  tni^jbfl  l«Mforf  ftiajtor  t^lci^t^  flhalts  ,  toS 
icjM  p9b  cJtertt«{r  iMpcn4  filfilcc  tiik  jj^dfimMr 
jplctti  AC\  i|aam  ^c;  *'    f     '    .> 


»  * '  't 


ilk  fii^  phM  ukimr  f  fiiiitooC^  )%rA4v|  UMif^  'AtMt 

KAin  defecitdcndd  ptr  J  C  acqoi^tret^tahdeih  \  ^i|M^ 
JbpIU  i^eqyiendieQi^ri .  j^  >f  J3  {  ^  *r«0f: )  .7  ccbui  ^bsA* 
eahdeih  dbtii^  det^ehdbtldb  per  'aGbVcaAq^c  )pIaiDi% 
4dbd  bftehdb  :  !h  d((dth(b  pkt  0  £  AcqUirit  *cchd%iA 
tdctitateini  ^ih  iiadbhdb  AiJr  tf£:fh  fPtihrra^  initoc' 
acih  i  quam  Cadehdb  ttdr  Efi  dchl(|ttle  ^  f  C  ItCB^ 
rfim^  tMdfih  i  ^balh  ^«tcU^Bhab  jpdr  J^V.    JBft  Vtitir 

i£4»  £/4«  Fcs3  Jg*ih^i^'ii  A9^ 
irg^i 

•  •  « *  • 

•mtiuit  «ngtdi  £,  F;  €  ?      1».  I^  ad'  fhMMl  j 


fH^onAnoiin  cbiM  dtdetlim  Mbti  n«5U^|0ffir, 
§^  USmr  s  vioi^  %i.  fckfitltcfik  iii  finaqiii  cpnr* 
pan^  ainifliin   inajoritn  non  «He  qntnutacf  infini^ 

tffinit  lecandi  otdinif ,  qn«  colUeinni  poreil* 

«         •  •  « 

(V0/&  iU.  (^\imv^  com  confi^cnri  poteft  M 
^mpodu  ex  ipfinitts  p^it  inclintm  i  qotre  tnobilo 
por.  cor^ani  continnatn  de(ccndfndo  tx  ^  ia  Ci  tcnt 
obdoebtc  velocicaceni  ^  qoam  obtimiiflec  dt&tndendo 

« ;  ^  a04»  ^  tiPfHi  itf^tn^  fimAC  UmAMM^ 
Hm^fkni  it^iuuiii  r^  td  umpm  Jhfc^njm  f€f 
A S  shkmHmm  jjmd^m  phm i»iACi  AB^ 
fHfkTit  sa  Si  t  stt  AXt  AB.  Dcm^ 
l>e(&enrus  cbfpoiis  in  plirto  incliMto  e(l 
ijMiifdf mitef  acce|cratui  ;  luti^  7  Tr  U  ^ 

«odem  timpore  decuftituf ,  quo  il  jB  bpCii 
perpendtcufari  {%. t<^ Pr^U L^i \  indeTT/ 
U^  4Ct  AAi  dim^^AC^  AB$  AD 
1WS  contiiMMi  pcM^MrrtoMiitt  (h««.  ACi  AB 
'^  ^ABi  AbiHd.)ii  prtim^ACr  t  jf  At  » 
^C^'  AD.  Ve!  ideo  racto  ^ltera  alterV  fub* 
ftittfi  poteftj  Hil^ftieariot^eTaa^a  obtinebirur 
TT:  tt  =i  AC^  t  AB^  '^  8C  utrinquo  radi« 
Ctm  csttrah^do  7:  1  ;s;  AC^  AB^, 
.  "1 .  •  "  »•  • 

4.  .  S^l  DM;  d  foe|ikt  tri^  contindt  prdporcio* 
nakt»  e«.^.  #  1  ^^  ^  1  obttiiiri  banc  pcpportl<Hiciii  1 
4 a  I  ££  ss  t:  c.  S\tn\^d:  b  :=:  b:  c\  babcttir 
H  (?  s3  ib.  ttAtL  irqotllA  per  candeni  qoafttitatem 
j|^ltipl|(^ndo  obtinebanir  4«^  iss   aib\   dtniqot 

&J||€fMio io propbrtimtiii  fittaai  bh  m  oi^* 

Ctra* 


C^>  h  Si  plara  ejatd^fMtiQtnis^jdiibi  dil& 
ptiuioniiti  longinKliiics.  .-•-*. 

OrcU,  th  Yeippora  detcenlKi  ^er  ffgtntfntii 
quaruitivis  iimUiom  ,  Q^  %i  bortzonrem  itmilftel^^r 
^cHnataram  perimetros  fimt  tn  mnone  (ulM«pilttt« 
'^uoramWs  lareruii^  homoiogorqmt  Com  ttnm(  tn 
motu  oniformiter  acceiersro  T :  t  s  l^  S  t^f 
4$.  t6o.  CeroU.  VIL),  crit, (  in  fig,  fe.  &  6i.)  T;  t 
=  ^AC\Vac\  c\\mqvii  ACi  ac  ;si'AM  t  ak 
s:   BC:  *  c,  fief  ilcniu>  T:  ^  ^   #^^#;#%f-)t| 


'  C(»roS«  711.   Slmilct  fircoforQm  arcus  Ant  pleili 

iitAiitii  fimiKter  indiniit ,  qcMfe  id#m  mobtie  lieVtif* 

'.r«r  arcos  itmitoi  trmporibos ,  qoc  (tot  in  rati«ne  fib« 

dajilicatii  hprnm  sr^aomi  «ot  rfldi^ntm  «plii  fgBfifM^ 

iionaliiim» 

§.  20  J,  Tffnpuf  difiinfui  ffr  quasvis  ch^^ 
iiAS  tiuuli ,  cujuf  diamttcr  fii  'ad  Borizontnn  p$r^ 
pcndicuUrii  ^  ^quitur  'tcmpori  dcficnfus  pcr  ip/am 
diamctrum.  Defcenidat  enim  mobile  per  Ad 
IfiS*  ^h  )i  dcterminabtf  petpcndicolaris  jB^C 
(  nam  angulus  ^  C  £  in  femtcirculo  redu; 
td  )  fpacium  epdem  tempore  oblique  decur# 
rendam ;  eritque  tempus  per  AC  ts^  Ccmpo# 
ri  per  AB  (  §.  202yPr§bL  /. )  .  11.  ob  paf al- 
klas  ifC,  &  J3  0iti(]«mangulus  CJ^pTcAtfS 
cft;  proindeqtie  DB  perpendicuUris  ad  CB 
rurfum  determinabic  ipttium  codem  tcmpOf^ 
redecurrendumi  qoo  CD  :=:ABi  ergo, 

"^  Bb  5  .        CQr%1t^^ 


;r. :  fCMEi  Tmqpm  de(cen(iif  f^  fsumk  chmi} 
«jflnaip  Umr  (•  991111«  i  9^nt«r  wim  icai^«ri 
4f  ftctnfiif  per  ^iiiQtnnioi^  Cm  iweii ,  «xifliipct  i 
«qiari  fimiUter  tefDpon,  4e<cenr«i  per  q[^vis  fnioi^ 
vr§fi  pteoii  mrm »,  ^m  pra  cboriUs  hfthm  poSnt  ^ 
r  •01,  nrcui  ninfaii  ebo^4i&  ^Midetn  (iiU  fm  \o>v^^v^ 
€in4  f$xp^  (uDf  ^  tt  noh  pelition^  t  ^«^  pva^QJroQi 
fi^KQmpitwi  incliQati^c  ,^  %  ^ut  pcii4iir  g;r«?iqi 

H$«  aQtr,  CV^  i$fc($iJm  /yr  /fMiMi  l^rll« 

^$M4$r$  9$up  i  naoi  celcrtus ,  qium  mobtlo 
in  fine  pUni  inclin^ri  cen(equiiuri  non  con« 

,  tiiiao  Deric  >  (ed  Ti  inerri»  confervetur  j  or« 
go  DiQbile  coQcepiQ  inipeta  ed  oindeofi  paf* 

•tii  oppofic«  ehkudinem  oioto  retaroeto 
eftondeiie  poteft .  fi  it«  diroAio  ferat ;  0,  c« 
corpui  OK  4  Updini  five  in  C,  five  in  #  ,  o* 
fceQcJ^ro  pQc^ft  «d.dUitudincni  C$^  ycI  Ci^ 

[.iAi  tempor*  afcenfui  rctpondohum  tcmpo* 

*TiQW  (^efcoQriis  pcr  pl4Q9/«ii/iMr  indiniUt 

SfiiK  Si  mebite  defeendoiif  vi  grivic«tls  fi^coa» 
^um  ^jndeip  ^  sQt  psritllelam  dire^ionem  perp^Hui 
isrg^rur,  «eceieratqr  niotiii;  maoet  enim  celeritis 
«equifita  ,  fi|  nova  ebnrpiranti  centrntiQ  addiciir  | 
COfPi^ue  gravttas  In  v^dnl^p  noUria  cbnftaHf  fif  ,  mo- 
fcjlQ  atqoalihiia  temporiboa  ir^alia  accipii  ceteritatis 
inerfeif nta »  aileoqnQ  niotns  onfforiniier  ae^leratnf, 
A^^  ^  gr^vicat  in  eorpus  jam  tnoturo.  perpetuo  ^gili 
contrsria  dire^one  ,  ^(}<)aU))Qf  temporibns  $^uili« 

fynt  ce^Ti(9ti$  dcorementa  »    motusqoe  pniformiter 
1  etardabirur ,  non  ante  extlingnendus ,  nifi  cnm  mtt 

,  l>i(9  pcrvcntrrii  a4  esm  almv^dinem  ,  t»|  qu^  ^S^ 

cwv 


re<iitQ  corporis  saQalibos  tecnj^ribas  cqoalei  cete^ 
cttiigradas  generet,  &  exfHngQtt ,  debet  in  D\  dc 
t^  m^&M  ,  iliisqiie  pQiiAis  liiniHter  pofic»  idesi 
celeritatif  grados  inveniri.  Jim  ad  pmduh  ^ifMk 
fiido,  qnorQin  tbeom  manifcAe  derivitQr  ex  diAtit 


$t  Sd7«  Si  pendukm  $it  punlh  ^uUtii  ^ 
UuiUr  inC  (fij^.  6^.\/ibi  riliBnmA^fiindef  mom 
im  mniformiiir  ^ccckrato »  €f  in  B  Mc^uirii  rmk 
pt^riiatm  »  fus.  mm  rcmd^  4^bmdirc  fojb 
$H  D»  Oum  eniin  qoiviS;'|CUi{i<jras  cpryx^ 
cus  coniiderari  po^t  ranquota^coinppQcu| 
ex  intinicis  planis  injclinads»  inOnite  pairfi^ 
poterunr  cuivis  arcui  2CCQfHtM4^n  t  Sl^^^^ 
tino,  atic  plurilHis  plaiiis  iodiaesii  4^  ^MKI 

•t^l;  ei^o,  \  r     ^  r 

f.  208«  OlmtSi  per  fuemvii  drcuH  jrflMI 
CM  (6p6$.)  in  B  4€qmfi$4  $li Md Hl^^cm^ 
^na  t$f^m  fcrpcndicnliri  f$r  Msm  diamitrmif  AM 
e<f  tfirersnfr  ,  ut  clmdn  CB  nd  diim$$rnm  4  il 
Du^atur  enim  C  m  perpendicularis  ad  4^i 
erit  celeritas  acquifira  per  arcum  CB  hz  c^ 
ferttiti  acquitieac  per  mB  ($«  903»  8c  ao^.jj 
cunHjoe  celericas  per  m  A  m  ad  celeritatero 
f€rd  B  UK  r  m  B  id  f  AB  (  h.t.  in  «• 
tiooe  rubduplicata  fpattorom  $•  i6a  0»ilL 
yjh)  etiam  celcrtcas  per  C B  tfft  debet  a4 
Cf^iericatem  per  i<  £  ut  r  m  B  ^d  r  A  B% 
Elt  vero  /^lum  ACB  ^  Cm  B »  e^eoqU^ 
if  j3;  CjS::;^  Ci( :  «tj^J  proinde  >4fia  ;  Cff» 
aAB.mB  {§i204.Sek$i,)^6f,C9'^dM^  r 

Bb4  •       mSi 


n 


ThJJV  Y  AB.  'Qiioniam  *rgo  cclerira«  per 
.CjB^ftl  a4 celeritatcjm  ptr  ABut  fmB  «4 


r  '  Or^fff  Si  celcritatet  pcr  pluret  e}usdem  circoU 
^eoa  in  pando^fino  £  aeqiii^r^  invic^m  cdfiif^raii* 
far ,.  iienio  non  viaet  fore  easdem  inc^  fii  ut*  iiitlt 

boruti)  ircntnn  cbord^  CB^  &  EB^ 


•/,  » 


f •  809»  TSfw/wn  ikftHtfut  f0r*JmSu  du^ 

rum  tiriuhtum  ^m/  CBu^  Sctfii  fig.  64.) 

jl&iff  iii  Tdiinnlf  fi^duphcAtn  hrum  muumi    St^ 

.  lAinet  tvAm  «ncuf  futir  pbna  infiriita  rtrtilHtet 
fnciinata }  afJ^dpfiied  decurruntur  tcmporhp 
9&t\  '^W  iHf  itv  t^aetone*  fttbduplicSkta  rpa« 
fioruiHt  (eu  longitudinum  (  f •  a04«  C^i"»  M }  i 
|W|50  «fi.m  arcui.     .  3, 

ir*. 

Tl^tm^^fm  f#  r^tti^f  fiUf&flkmtt  rndhrumi  ftnt  cnkm 
#cos  (imilQa  m  rs4ki  ,^  id^  &ft  «t  IpngituAitif 9  JierROl 

/  ##..s:,  i  » ./;  enT^;  t  ^  l^hl  ^A  Hinc  iain 
;ile  non  eric  dacU  tripufi  boruiii  tcrminorut^  ii^ 
t«iiir«  qu^rtuni* ' 

'  *€.  ftto,'  ^umtH  ofiillathnHm  df^nduHt^t* 
V^fk  ^ionptudinit  ^odtth  aliquo  ttmpori  eotffiSif 
i^Um  funt  ik  r^tiont  rici^ro^a  fubdufilifat4  lohiitt^ 
ifriffJw:*  namTuttt  numcr?  ofcillaitomtm  rtci« 

Sroiqe  ut  tempor^»  qu4t  funtin  ratieine  fub^ 
'^rpligara  long5ti$dlnum(§,^ri^.Crtrf )/  etrgd 


V 

*  'g<iM,  Nomtroi  ofcilUrionum  tffc  Inftrft  iit 
temport  ex  co  confictfur  ,  q«od  ofeUlauQnuin  nom^ 
rus  cflf  dalcai  co  minor  ,  quo  m^jus  tf  mpvi»  nngul» 
picilUtionibus  pmgcn^is  impcridi  dfbet--  l«f«ni  w 
tis  rribuf  icrminjs  facilc  dctcrminafcttttf  utriuthhct 
pcndiili  fivc  longitudo ,  feu  numcrQi  o&UUtionumt 

§,  sil.  h  i/ifhroitif  dwtrf^rwm  fniuhn 
rum  •f(iH«tiontbu$  vi»<*$  '  ffrtvititu  mtlfmieit 
fUMt  ut  ptHduhrmt  loHfttmlmH ;  fimt  «mm  ?i* 
fes  «onftanws  (  qotlei  habentor  m  exiguil 
4b  •ad«iti  ftperficie  terr«  diftamm  )  propor- 
ti6n»rx  fpatiis  eodeni  tempore  defcnptis 
(  §,  aoa,  CnroS, )  i  fpati»  o(ciU««Qt>ibw  ifo. 
cfaroais  confeAa  funt  arcu$  Umile»,  iivo  My 
cnbrt»  fimiiibui  propoftiwiale»  «dii  j  radw 
fynx  jongitudifies  pwdoknw»  $  •rgfft 

fendulum,  9n$  fpidnh  ejusdem  lotigimdiuk ,  V  ^ejH^^ 
kt  Arm  4mrmti9  ificbrQM  fjfe  Mcnti  ioiwc  cmni 
hypo(hf fi  ^  i  /  s0  ri  r« 

'  Drf ff.  II,  Erg^  R  fdm  fend»Itm\,  Wt  fjusdtpi 
hifgimdi»^  ftndnta  in  vari/f  Urrs  hcif  ifocbrm(^  nm 
fnnt ,  vis  gravitatM  emftans  mn  efl,  Ubi  plurcs  hu 
Wrnr  tjwidnm  pcnduli  ofcilUrloncs,  vii  grJ^Titati»  mj»; 
jor  cft  j  ykipfuciarcii  mlnorcft.  Hinc^.  l^i-  ^h 
fir$JK  docui ,  mniotcm  graviurcm  cflc  /»*  f^^  ^^% 

Sehl.  l  Monul ,  moncoqne  lw«m  t  Wt  *if 
ttmt  ad  pcndulorum  biftorlam  (crinfl,  ftrlp»  »•«•, 

tcm  •hftrahcnio  tb  •dion^is ,  C,  C  JWWIJK  Wg^  « 

rt^flf^fifi^,  0emri/ffletm0^  €Mf^     •^T' 


; 


\ 


niiUa^  habercntttr  ,  pciiduli*motas  fem  pgrpcnioSy 
j(fL  omutoo  ax^6liffimuSt.  Ineem  Ycro  propcer  mcd^ 
Ip^flftciHipfn  ,  *fii£lioncm.  &c.,  (iicccflive  mifiDimtvf 
^iUMioneSi  dpocc  fciiiim  pendoluin  m  B  conqvieftat^ 


i^^'<> 


&W.  tt  Ad  o(ctiIacioncs  ^endnloraai  reroe* 
fhrnrfim  $laflicamm  agitatiot^s  y  de  qaibot  p«QC«, 
fni^lUgb  iutem  nomine  fibris  eltfttc»  chordm  renai£ 
ftiHMiM0H(;^46.  ),  «qutbilem,  &  fortcffvM^f^ 
M«iy  qe:f»09a(»in^gnc«i>,pfod«t  fbfttcit^m  ,  filbtiir 
de  vero.nimis  ftcnGi  etndcni  fKBrdsi*  Ejacmodi  lifari^ 
Ku  fiiamentis  tfnuiilimis  intcr  fo  conjngttis  COQOipi- 
mus  CQt^fta^e  (^ippis  corpori.  flnfticn; 

*  .  • 

ir«  Si  *  itbi**  siicufctt  fidrffiis  ^ ,  &  iB  figsntar, 
mdioqtie  ejtis  punAo  C  sppendstar  pondos^  iBfleAcrot 
f hords ,  &  sblbit  in  6nun  ^  D  &  Tam  fi  fbirds 
tfn(^  qoidfft)  icd  nonduai  \n^%m  mfdiaQi  pundmil 
Cjongstar  cum  mcdio  ejosdcm  diordsr  po(bn  flezQ 

Siinfto  £1 ,  r^£if  C  D  ft  punQt  conncdcns  dicitaf 
Agitt^»  Si  d^nlqqf  centro  B »  rsdto  B  C  de fcribstnf 
iircas  C#|  fs(hibft  Or  qasntttstcm  »  qne  dimidii 
ehordti.  BC^  pcr  (ai  inflexionfm  prodajlts  futt.  Or« 
Ao  jsm  pofcit  f xsmins^e  rstionem ,  qosm  ed  Inf  tceni 
^icuni  v^  flfor^am  mdeftf  x;i   t^  vif  €$n4m ii(/Mke# 

m  t ,  figitu^  D  C  ;3  $  I  hnfffuio  cbqrda  nandttm  ini 

III*    P^fif  figink  mtmodum    9%^  hobmr 

'I  "' 
fn^fih  f  /U  f  5*  s  fi^^f.    Slvf  t  Sfi  vU  inJkSm  oi 

#•1  f^n/fm^  (  sntf  inflexionfm  )  ,  m.ihfk.fimtta  ai 
Hmiiim  ikori^m*  Vis  enf m  »»rrf  tfffihf$$  cxhibctut^ 
ftf  ff dtm  f  i^  ^  quftrf  cum  pdfits  %{tta  sdmodam 

iMtBlficf  I  s»  ^^'ss  4^|Cli4Mii  vto  tcndou  exteM 


Mliftfifttii^i  MciA.  Vktwtii  *#«*•»  igjl 
4ir<«timihiii  i.4>  &#<<;  ^«Mrc  compiitQ  imciUitof 
^mQi0  4i%iiiri  pMA  p«r  diigoniWiii  u  a  r  4 

i 

Q«li  Mlam  fliidliacQfli^ftiilt  Mq  ixirf aMtriMB,  hiu 
Wtiir  ft  li  =s  -r-i  proiAie  4ii  «  <-^    H  Vii 

Conqiie  imtiemnr  Tit  tcn^em ,  dt  io&rftenf »  wed| 
Jirvcm  e^tnhm  rationit^  ,  fempir  fitgitti  exi^i»  ejtliii 
4cin  alicttjni  chordc  «wnibtv  e«(Unii  Viriboi  enim 
iri  imimiratis,  ut  $ttmeH  tm^tuaut  iH  eadtm  r^tiqtt^^ 
Qporrif  ouin^Qtf  iadefn  lon|;itttdiQc  cliordflt  Qieniri 

l  *  " 
ciidcn  figiltif ,  ftcoi  qpq  hihcbitQr  ^  M  ai  »  s;  «^  k 

JJi.  Si  Gonfeniiifar  dnc  chord^  «^Qe  ioQfCi  &  tf« 
^oaiitcr  teQ6f  »  criint'6gittc  mtniinc  in  ritieine  wu 
fiam  {QQe^cQtiatQ.  S^mnor  enini  411:^  t  '»  Q| 
fuprf ,  Qaati  cQlle tif  dq^bui  Ohrif  erit  1  £  t  M  ^al' 
4 .V  T;  4  M  ^  STt  19.  Camquf  exhv^*  T:si9 
0; Ltss /» «»1  lii  53  5f  |.  Hiioremi  iftod eciam  fm 
linet  9d  ^hoi;dif  iQcqoiltf  diimetri.  U^9  Si  diTitfit 
iQngitudinif  fibrc ,  timen  «qaalit^  tenrfl^  invicfHl 
conferanrap,  erom  figittc  in  retione  iompofiti  viriQQi 
inileAentfam,  &  longitudinam.  Nempo  oft  !£  :  ii 
is  S  T:  st}  ergo  fiT^  t^  htbctui  i  £  1  f  /  «  ^:iii 
Si  prjifcieret  X  a:  i,  iOidibot  l>i  m  S;  U  HH^ ^ 
ilti  mtQifciii  lum« 

IV,  Cb§rda  AB  metmp^  tt^fiM  M^^^f^iM^ 
ib  tami^  fibi  rtUa^  cfiUl^h  NlQi  ?i  lUfticitiltl  Sm 
ndit  id  iitunfi  priQrem  ;  rcditqoo  motU  ftlRpir  Mk 
^elcriio  ( (eu,  qaod  vii  eltftici  nan  ;ikQi  i^Qi  gflVi%. 

m  igir  pf rpf  tuo  i  &u  f Qf  d  ooYft  iitoitM  idMWOMi 

•  ii 


i§4       mm  Ofm^i^ 

Cind«S'rtniitri)H>ffcr))  obriiitft  igimr  mixmMfn  ce» 
rittreAi-  in  C,    qrtdc  fii^a- «licriori  «scttrfione,  iy 
^gam  oppofirai*  irc  ,  irmimque  argemg  elifticitfitie  . 
Aitei^  cm  oportebit. '  %  i     .      -    .* 

«y^    AU«  omiico ;  ^fMr-  peMcm  a  difortt  tydaUks  \ 

«ojtit  con(tilto  non  memtnt ,  cani  ejas  applicatio  ad 
llminai  jam'  f#re  anriqiW  fit  ( teile  P,  MM  ) ,  & 
oicillationes  in  extguis  arcobus  cirooli^Gicis  i(bchrou# 
4«pr?bffldanror, 

'     ,     CaputVIII. 

l)e  motu,8c  prelHone  fluidohiml 

De  prc0ionc. 

^^»  9T3.  0iiiii  dtxi ,  qaae  iropreflionl 
hym^  .levt(nnti«  facife  cedonc.  PrQri]fl]m«e 
UliiU  cedionis  ratio  flifScieni  eft  in  particqU* 
rmii  €olMfion«  um  extgita  ^  nc  £iale,ab  in* 
W9f  m  (epaceri  po^u 

Cor^lU  h  8i  panif  fiotdum  compencntci  facitlir 
Ipo  ff  pnrnmar  ^  pot«(l  alin  flaidi  portio  in  iftam  ,  «lii 
in  illam  ^  pUg^m  movfrl ,  qoin  tor$  fimnl  nmflit  in 
iiin4em  pUgam  ab««r,    Comrarium  obtinet  in  tbliciiffr 

Or»ff.  /I,  Si  gemfn«  e;asdeei  Anidi  portionct 
in  diverlas  pUgM  abire  poflint ,  ppr<^rit  quelibet  fltii* 
^*  pnr  dSftiiiaiMn  «Hqqatn  fondi  portionem  prcmerc, 
Iflrin  foia  iimcil  .  maira  eaitdem  vniis  portionem  prev 
fMU  Qtnre  <|R9¥is  Hitidi  porfio  ,  independenter  ab 
etU .  eK^rere  porerit  vim  premendi  fuQdom  vaiis,  vel 
/#rei  I  foo  emtrinoidrf    R(ir(iif  ^  oppoficom  lubetQr  iir 

ftli- 


■V— 


\ 


Ibll^i r ^Miittm i>irtmH|M0  ^.HMP^,  1rtlc.^Acil« 
f«t,  tOMii  &UdMifr(«t;'ib  Ja^4«9i>^l|fkOttet|.Aut  &# 

ftentiU   '     ' '«  .    '  ".*  c*  .  ••  •»;'?-•  • 

tetic  i  6itq]u«  impreinM^  ficilc  ctt4unl.|  &  ffciic  tno* 
V«titur^  of>orM  MsdcA.  ^Qih^kMf  i  l^irigMti^  v  A  id» 
modttf»  fiibtilcs  tSk^i  mks^  6tm\m  ot|«r>«iiua4  ,frif 
atd^aiut  i^ii^kttdo»  t»(Mtr)  k«p«4i4|nt<^*  S4ibtiUt«| 
fardmil«nita  niiiiifcac.  d«dy«ifiiir  c&.^ii  .onod  flaidA 
ft  iie  tit  mgaBiSim  eAngor  ttfn  itiicirvctlc  uiiiiiticttt  | 
lliiic  ikfc  itiflchtQt  cofftMTis^ic  intWicicMli 

ikf#rdritrr4 }  betiiogtnea  ifMt» v '  V^  qm^Mil 
hetei^ogenMi  qusdivtrraef  fim^cSW  » 

tiU.  li^Ji^  Ctu  JlkUti  ifiinUjrMtk 
fint.  EltperiiDur  &i}e  Vis  gtibctin^j^ttjdti  pt& 
tkum  gfavttti  cflei  nttam  vactittin*.  mc  moaf( 
U^uU^  muU  gtst^U  fim  fpUbu  iM^d^ma^i^ 
fid  (^  fif%uU  UfmJmm  mtimU^grgim  /imi  | 
nam  gravitas  ttnioi  tnilTii  oritttf  a  KtavttaM 
fingttbrtim  partiatn*  ^ 

$1  215.  VpiJa  emis  fnmunt  Mrpctj^ 
pi  fii^ffd  p  fmkui  intumhunu  Naiti  4ray|| 
cdm  unt,  ttrgtnttif  I  ac  tendttnc  deoifrum  \ 
atque  adeo  vi  gr«vitaii#i  premuM^rpora  b* 
M  (ttbjeaii  ftujMMgiiMra  fii)t#  fivt  tm^gp^ 
mi$  Qtiare  &  fimdlii  vatirpiemitiir  a  fkii* 
do  i  &  (]U«Yis  tnferiof  fluidl  portto  i  Ap» 

fior«  iibi  incttfflbeoit* 


1AII&  DiMkilfMli  Biifc-|^ilti  li  TMrftlil  rinbSi»^. 
Miit,  iqtf  em  tdmjMrtMt  flraii^  «ilai^  tsjpimtti  nM^ 
li  plhspefrtodiilii  Vi  t  ptU»  ^ttolli^  ^mdiii  fHlri 
ttqiMtii  Vtrfiil^  (  it »  ciitoi  in  iiltili  ts^iit ,  (^trdpi  cjos» 
diem  t^dndos  ph>^ftntiYM  fttlkk  ftuli  tobicmiv  elti* 

itfr#)  lu  t.  Mtt  liiti  deo^niili^  Hi^nt  ptAvittt  Coo  prc^ 
IMre  MtiricWl  IM  ftt^cftril^  CJMm  ivxm  fHr^m 
iK>v)i«iActiBr>  in  ^«<jpiMi^%iaBi'4chMr  ipcacial^rc» 
VtiMt  fpcdfici  V-  '  lObrMi  rciidliit  Wellcia  fd/Sut 
yirfiii  nmtentfii  nviii^-y  4^ihc  Jcn  flccctiliortini  oMniiiii* 
nis  cR,  #<lifiriwM('  confiroiciiim  e«  c    L  Qvocwnivi 
bi^o  cti^nfificm  liqnidc  pohdui  iloin  hihcnt ,  &  grcvi. 
feiicm;  pliiiAdt  ijQOMll^lft^oti^  Cbhlillcilr  >  iiirjgentiit 
lia»rilkipi|«<ti^;prtnHnt.  •  IL  Oiimt;ctrpii$  nirilni^ 
itd   ecntrtiil ,  Vfijf^s  c  Xfx^  ji^cft  ;  j^itur  j&  fluidc^ 
lljk    ipiuidc  hit&htut  cd  cchtrum   uiiuni  »   ^oaihdia 
JpBl^.^r.'wr|.  ic^  pr$pri^i  ^dhi  pcri^  hiicnthr^ 
thifn  &nt  tis  iraprio.    Sahi  ih'l6cO  boh  ptbfn^  ton^ 
ttttftc  hiilillittt  ntttHcifh ;  ^ilU  Kigul*  n))iddl^in*tn6^ 
ti«itlli  gtivcr  fbht  \    it(|hi  lliAipcV  gtc^ts  filnt «  1)toi 
lelittqiis  ioei  teonfiflifit  llclldc ;  •iiqph    IV.  Httm  cvisp 
mmt  ixptf imtncii  dfc  ib&rfiiilritBf  quolldi«iig :  Mer^ 
ticiit  ct^  lii  mW  iTorMccUiipiCt  4j(ccndit)  ce  deftens^ 
itl ;  koh  ctttcih  itccndck^er,  htfi  if i:  |ircnicntt/    ddo  i 
(fittillilir  ih  tilbiV  ctihihahtCciitiliiis  l^tf^olVltur  Um^ 
dlic  db^cqic  t  oieoj^  lloIdiMot  itiii  fpcciSce  ieviorf- 
tttt  2  liifi  Vcrh  iqic^  i^ietifti  dcc.  gtaVitsr^nt/neUtiqticnl 
Mthnefletlii*.     |tih  t  St  TphkH  ciVa  ^  fed  in  ibbntti  ib^ 
lohgiim  difthchl  ittt  eV«cnetM,'«  c^uc  iiAilhetjis 
m,  cfNlldft  i4ilh     II tolrtiitti  Wtk  c&etffionis  %(t  ptei^ 
iio  iicis  mfitt  iiiOililiciit!»  -^^  t  Mcius  tft  poti'd«| 
%ifiii4ni|inr  1  ^m  liiil  ihiiclp  i  etgo  Ut  grcvitah 
Mifl  Vci  NHIili^  jMiiiiilinliierfillh  ));ond]prcthr  r  tiih) 
Mdtt  iitfUC  fepietilttl.     mji^rebehlletbr  jpohi^us  tlhti* 
mifiii  «liciitwi  ipfcfMlif  iihlirsy  ^jb*  m  idiihpltt' 


Dtmitti^fiddorilfnt.  Iff 

■  •  ...  t-      '.7- 

^t«  Yttne  tttain  profiindiQs  fliergimf  |«gttli  .tqnii 
rep)et«|  qoamva^aa;  crgo  &  aqua  gravhati  .  ideill 
•fto  dt  fltiidii  aliis* 

R4ti9m  aivetfirktuin.  f.  Si  llqoida  graVitafli 
In  loeo  proprio ).  debet  ppndus  Hqoidi  gi^nVitantis  (eCf* 
tirt;  nott  autem  fentitur;  el-go.  Pr.  m.  qtii  Otoiaftl 
6  poteo  trabir ,  non  (entit  potidus  aqo«  fltula  coiiteii^ 
Ut ,  (ed  neque  pondus  aqoariim  litoldt  iihminentfiim  % 
«nt  eerte  qui  (itolam  profutidios  aquU  in)itiep(am  tt^ 
hit ,  non  ttiijtta  (enttt  pondosi  qoant  ^iii  initios  pro^ 
iunAe  aqt^s  immerfiim  |  eoiii  tamen  pro  di(pari  ratidii 
ne  colonmarom  aqtieartiim  iltols  incombentiom  po<^ 
dos  diipar  (entiri  ^eherec  ^N  O.  M.  debet  liqof» 
4i  gravitahtis  pondos  (etitlri,  nifi  qoid  obeft  C.  M.  ft 
dbett  N.  M.    Sie  D*  M.  ft  N.  C    Qtto  minos  aotes^ 

SaVitAntis  liqtiidl  potldal  (ctltiattir  |  obeffe  (blet  teqjd» 
\rikm^  qopa  iil^^  tifutdutn  prMvitim ,  &  tpbnnM 
UtirMhs  jntercedit ;  tiam  ^  tit  uifira  docdk> ,  qoantonl 
gravitans  portio  iiqoidi  ticgetitr  deor(}itti ,  tantam  tt 
Mtomnis  lateralibos  ot^etor  (hrfiim;qtta  *quiUbrtta|tt 
eonftitata  liqoidi  graviMmli  potidtts ,  ac  preflio  omtfi» 
M  (etitirl  neqoit.  Nempe  tra  res  te  habet»  ut  //i/i^ 
cihi ,  quarum  tmi  gravilfimis  quidem  ponderibas  cn 

liuAa  r\t ,  fed  dtieri  dquilikfdta  i    tnC  eflim  j  onofiil 

huie  lanet  matiom  (oppohe,  pondos  non  fentie»^  Ad 
fr«  D.  t.  p<  A.  non  (entlt  potidus  aqoa  fitola  eontetu 
tlft  nee  aqUarttm  (itubfe^ilicombentium  e^  tf/AMi  ««^ 
qttitihriiattnk  C  h.  p*  alia  de  caotra  R  h.  p«     SicDi 

i«  p«&  N<  C  qminttttitetinqite  fitala  immtr^tttr  a^ 
qnis ,  (emper  eolnmna  aqoea  fitnlc  Ineombens  !n  ns 
qoilibritate  erit  eom  eolomfiis  latendibos  ^  Oc  pra  Afl 
(Mirl  ratione  colomnarom  aqoearom  fitolft  Ineumfaen* 
tiam  itidem  diCpir  ratlo  habebltor  eoloiniiarttm  late»^ 
ralium  ,  qo«  ctdetn  nt^opoftlont  ere(ctmty  ant  dteN»? 
(cttttt^  ^tta  <oloffiliii|fittt2ir.ilitttm|Nimiii  ^ 

'  •  ^  i^      *■      *  .  •  ' 


1  ^       Mi$  tL  e^,m. 


tU  Sl  ildMi  grivttdit  p  nec  faifrt  tq^  l>H« 

IfTtif gcre  i  t)ce  pircos  nattre  i^  ticc  armatorct    tif  \m^ 
hagiierullii  iQt  inirioiti  CMilllere  |)orerunt;  eotnpriA 

^mt  enim  ^(^tcbit  bcrbiSt  inCncs',  i&  urtnatotM^  «tl 
Vigenci  tnoit  iqoiruin  (ibi  incumhcntium*  Qi|in  eti^ 
fun.  ektri  flqpis  tief^  iion\ines  piogrcdt «  nec  av»  vo» 
)ata  (uo^iCfitm  B^^dmte  polletit ;  urrtsque  cnlm  preflio 
jier^^  f  qu2  muTtorum  cemenariorum.  pondus  ^d^qtiii^ 
iupcranda  clb        ^  6«,(cqt)<M*  SMuida  ftd<«  aqiiu 

■^  \lpftata  guvitarent  ^  aut  \ito  graVittrent  inaqUahi/itir 
^»  fc<|ii«  M*  S\,aqtiili6rata  grtvitant  j^quahiliptr  N« 
j^u.  JM* .  .$ic  P«  i]|.  &  N.  C/       Primuin  >||  ingcnd 

^  ^ndcrt  iqoaroin    libi  incamb^nriiim   non.  COmpri* 

^  inuntur  lierba^,  quia  pondul  tncmnbentis/coiofnniK 
jlqdec  Ibftenlator ,  atqqe  in  ordine  ad  aiQltun  clidi» 
lur  i  coluinnU  laceralibui  ^  CUt%  quibos  atqoilibrit« 

%  £li(o  iutcm  f  Otidere  i(tg  |dm  ^$dle  Hoti  crit  plat^ 
lis  io  iqoii  iflbrgcre»  HuC  idiiotandum  cft  j  quod 
palu0rium  hirbiruin  plurima;ri(iices  fiiis  noti  tn  fbndo 
fgotit)  (ed  io  (uperficiet  nafcontur  enim  t%  ftminibns 
oqoc  iOAitititihus.  Dtindi^  tiott  eomprimuotor  pifcc»*^ 
jl^  orttiitoreS)  cum  tis  ondiqot  itieumbint  tqoi^  ^tqui^ 
iUrag^i  qoarum  adionei  motoo  ft  ic  clidunt^  fil  igi« 
lur^ut  preffio  tquc  incmnbtmiA  ab  tquilem  t€ft$C* 
fiotiem  iqoit  jttferSbriij  &  columyarum  lateralium  i^ 

•  tentiitttTi  tiittrei  vero  urinatoriboi  iai^guis  per  ocO* 
Its,  ^«rct^  iuretque  elici  (bltti  jion  |quidtm  lh  tq,ut» 
tom  iiKtunfaet^tium  pon^cre,  (ed  ab  teiis  nimiotii  .i^ofia* 
|nrei&  dentit^c  ^^  prscipuc  ft  campant » in^  qua  oiinito( 

^  fonliftit^  ntmii  propere  Inti^a  t^quis  deint^tator*  Quo 
mimit  iotem  empMia  Ip/a  ab  immini  aquirum  <poa* 
4^t  eomfMrimatoCi  obeft  denoo  aqjiirotn  >g»i7/^H//if^ 
4k  cimptnt  !n  moduio  fornidi  ex^vttx  ^ra  \ 
tiint  ttiftm.mlpitiitii  vitri cimj)iti«  formtm  induerf 
ddbttlt*  t^/irm0  ntc  hoimnimi  j^rogrtitui  >  xtec  tvf* 
«m  volitol  ofatft  iiris  g^vltitio}  cum  enlm  griviti» 
liontiD  Hfli  otittrlvrii  tUdtt^griVitai  icrii  i^At^ 

rii| 


flflimm  fiipcf^^ctti   tttri^  Mihitttirlt  wtt  m 

«^>'6«%  i^fl^/tllB^  1«*'%  ^#q^  <>W>  m^y  \ 

jrfliU  libnitliiii )  &  t^nod  l(tt]^r,  p^Mo  ikt^marw 
Qttoniudo  jiiH  )plru|ridi  pdCt ,  tbjos  MMnWa  liiit* 
iDh*€  «liflb]Vi^:a»inprSnii  tnftevb  >  «rcjvic  ielbrtii  bjp^n^ 
Itrct  ?  Grcii*  cl)unlcin,  diKrdVcfciitut  tacntbiii  ,  fl| 
tDim»fii^ctchtUr  t)ifi  itsdcm  bi»  kniile  ^  &  tapliQi  ^ 
fmclo  ^jmtitrdta  IntKimhtrtut.  i>ket  IL  Sttiic^ 
tOliiniki&  UVtii  i)bti  iilki  IneukiibchlB  a^iiitMta  ^  fehtict 
ytHtti  diehtrit  tjtiiidcni  jpnhdu),  Mti  ^hs^  igoim  Iblife 
tiatUir  Im  BdlrtfMr^.  ify  SolUdohfeni  tdcbb  tA  eau^ 
JEim  MeiTurit  fivtl  «liatndtncts  ^  jBv«  iciSMIkfttii  tk 
iBirMictroi  ^ 

im,  thdvck-i  dcbeht  (  iiibtus  cnim  ctfcduii  cft  ffkviti^ 
fiohis  V  t\il  Vcirti  li  cjffefihs  hoh  tft  ^  faiibctbr  graViiift 
f{0>  lcctt  iiaib  llht  tjffcah)  .  koh  autciki  hiV>Vcmur| 
tfgt)  htc  ghivitiriti'      l)e.  D.Kf;  Si  Auiidi  «^tihfahM 

l^vtcaht  gritviiafhftJe  Wvu^  ftn  i^fiMHie^C^  Si  Iji^ii 
|^i4«yW  iMlirttii^  &  itmtacifer  N.  M.  C  kki.  &  N\  Cb 
6raV(hltiohchi  ViVahi  ^  ieu  cflicateekii  IjicD  ^  t|«ii  MH 
<lfeiii'ihotii  bdhjuhaa  ctb 

:  *  ^ .  I>ievl  il  Oihnisr  iJ^lriVitatiO  t^  pird]^  IMoM»  | 
«i^.  fi'ihidi  «quiliWati  itaVtMnt  i  IhDvCri  dcbent» 
m.  t);  Ai  left  prbpticr  motbm  itnl^hahi  fihcnl .  hblb 
tihi^tii  a.  A;  eft  lihicit  )5i:dt>ter  khbtuhi  Nv  ^  Si  C% 
(^raifiUtid  c(t'^i:6i5tet  ftrihiiitcHi^  jhairmbhiihi^  It  itoifk 
gldMticfhein  iiiiivlSrfi  i  ^b)  JShit  tuifi^iehM  bfalihtthf 
fti  litfth)  i  &  |)iHrffibheiii  fluiiib^iMh^  t)uahtVfi  l£khla 
■I  ^gMudci»  ^^ttlitti  «ar  «iriiiUirni  «tHffil  ivdhMk^ 


Miui«(y«if  pfftftnv^iitt »^lli<gSinit  i  '%l«fll  ^^^^^^HMt 
fmftfiKitt^;  IttUk  "conteqti^i  ;  >%iM*.^  % iinttct Jctiiw 
Pr^  m,  Non  cxpttiiodr  iaa}oiiKlii*fli^ttl^tefii^in  edti* 
ceoAi  fitult,  %f^m  pFofondt  $<fMi  t«imcfgitur  |'  qt|pm 
^lttdiiiniis  fltlt»      At<{ut  v)er«N»«j|9fi:iri  ^debtreiniui.  t 
MoCceus,  ttciQetlimi  iirnlaflt  pirofondiut  mtrfini   e 
ihndo  gltest  conftrtdo  eduein^ut^ 'i}iitin  duiti  minat 
|H!ofiuidc  merltm;'  ergo«      oqi»  Sitwtn  profundfbritttio 
f^it  inimtrfii  re  iffa  premitnr  magts;  q«od*tOfn«f» 
etm  eductRtet  non  mtjotpondut  {m^mt^  tribai  de« 
bet  a£(ioni  columntrom  Itteralioai  i^  &  tqn^rum  ipfe** 
fiorum »  quarmn  vf4  oiiim  aBqoiiihritatem  iiidiioivcomL 
lolorana  verticflit;pr:prfmtntOt     Qood  do  glaoit  ingob  - 
ijfcom.  eil ,'  iit  expedio  i  experimur  ma>arem  difficoka^ 
tem^^  '.quia  penes  giecttm ,  eorput  otiqueiblldoiii)  ^n^ 
cettdt  (uOt  vaHdtores  itmitet  cohsfionis  ,  qiOMi>>peiiM 
floffit ,  ^ioromptirtcs  fiioiUimt  icptraiitur«    ^       '    ( 

'1       .  >  ••'  l 

§*  %2Q,  Buid^  homoffniA  mn pnutmd§fiu9iip 
kuamji  componmt  aJ  Imllam  |  h,  f^Jf^j^f^f^ftk 

Oibf^cuU  cuivis  impreaiom  proniiJlitny  t^ 
^gIGis  urpnHjp^mriiMti  90  usque  deftmdttnC| 
dam  Uicot  'deicendefidi  ultra  non  (it^  ^  E(( 
vero  iefnpcfr  Jocut*  de(cendefidf  ^quotttqi  io  fu« 
per6ei#  horironii  perallehi  non-rum;^fcrgdt 
eoittqqe  de(tendenr,dum  fiht  in  fuperficie^ 
ri^onti  paralleUy  five  adlibtJhm^  IL  Finge, 
CQlumnam  aHauam  verticalem  s  x  altiorefiii 
•de  columna  ubi  vicina :  comprimec ur  fphx^' 
Snla  t ejutdem  coiumnas  «x;  cumqtteomnei 
p|usdcm  LtmeU^  partet  t^qualiterpremamin* 
oinnem  rcnfum^  «qualirer.  iiidem  premettm 
^hacruU  4^  ^q$  e(l  in  eadcm  columna  horis, 
,      ■      '  8on» 


\    » 


0r  mmJkUaim.          '4i| 
^_  ^  eatitr|Jtrii|iiifcM#4y!di 

primatof  ttnbol6|  qui  tX^Sin  f^jfizt  ipttt^ 
Tam  vafis|  ne  iilU  lij^uorfc  jportio  ^gredl 
poillc »  uMi^Hi  per  poroi  V^iis  erumpit  m 
q|tti4<)in  >  fi<:qtte^i)oo  lliinoi^gtr  comre  (ti» 
fKirficiem  tefis  fuperiorem  t  quem  «•mtt  lip 
4«r4t  &  fundum» 

«Jla^fc  Prtfflo  in  oiiiiicm  iMftci»  tft  ftcdkvle 
«fftfdlo  iluidorQfn ,  •  qua  pkroms«  HydrbdytmtilHe 
ylMrncHnent  pcttdcrc  vtdeotun  uolto,  ]MllioiftA4ik 
tlt'  cattffmm  mlniif  eicpiorittiii  •&  .  ^to  tsif^fi$hH$. 
$cill0it  t  etuflaffii  non  air.nino  t<rei)oiinur ,  qmt  coiti* 
|iiiuittoii«tn  ptrticoltrutn  elementtrioni  flalda  fompoo 
tiemtu»  noa  CkxiiiifikiB^  eognoiciinttt.  Scd  'itmtfl 
Taper  matcrit  iftt  (hiloropho  digttiffimt  tliqoid  difiK 
etndotti*  >  ^    . 

Ptrs  mtxittit  Pbyficorum  velettf  ptrttt  ioile» 
Mm  cicfncntarct  tilc  J^lidas ,  ^Mrm ,  &  yitiffcii  ftti* 
ftm  ^b^ritm.  Miiiat  tjont^m  prottdatyr  in  ittM» 
tom  ;  gtairifi ,  ne  frifiio  impeditt  tdmomim  ftcitttti 
^otom  «  ac  (cptratioftcm  tb  tlils  i  '^Urkm « t«| 
0htri£9t  fiMki  dieunt ,  qacid  liarc  i%ttra  maximc  ido» 
iict  fif  td  txplictiidam  fluidorttm  fummtm  oiobiliifti 
ttmi  &  mintmtm  cotittlioi^«  i 


An  molecultt  (oHdt^  ^  fic  (phcrlctf  i  e  qoibtte 
Atttdt.  ooticicunt  f  dnrm  fint ,  dt  immpriJlihf ,  nott 
liitis  convcnit  intcr  Ptiyficot.  Dt  Aoidit  Milmadtdl 
ctrtttm  luibcmttt  t  tlaiiict  dTc,  &  fom|ircmlit ;  itle 
Attidttm  Mf  tft.  Scd  qttid  dc  floidit  tlcniioribttt  ^ 
Oi  0«  oico  9  tqiit  I  viflo  ^  Mtrcorio  ftc.  conMfoctt» 
4ttm  t  Soot  f  qoi  potcnt ,  corom  ptrtct  dcflMi^ 
ttrtt  dm^4i  cflc»  &  iwMtfr^ilit.  Sie  trgttttnt  i  tt 
i§^b«re  tttftt  MiiSorc  4utdo  tmptcta  |  &  hcrmctico 

Cc  0  .       dtoft. 


$t4       Mttu  Cftthmm 

Prcffio  «11111 ,.  qotm  flatdtmi  ^crcct  ln  ftMi. 
dum,  ptnd«e«  -^•^,  ^^t^tituHittr  rekinnu 
twm  ftnmtMum^  ntmi«i>0'««(unin«roni  pt^ 
«Mtim^  CvMM  poiktktifk,  9uc«tid«it*r 
JMi«  imwiifo  eft  proporiiwiattf  crg»  pr«C 
i»  in  ronchim  pend«t  «  b«d « It  «[titudtiw  lU 
quidorum«    IL  IrtV«lntiiclin«tisliqutdapf«. 
«nune  fandom  MrtSlfi    tf  ma  gtwHm^^ 
«ft«utcm  gnvkm  ^bGAott  flatdi  hemogMei 
«t  vohtm«n »  (urc  roKditasy  volumen  priOiu» 
4if  au<  fyUndrt  ut  b«6tduft«  In  «Ititttdiaei»  t 
irgo^  pnSm  «ft  .nc  bafis  daa«  iti  «Itita* 
«kncm» 

r&ppneioMt^  ^ dt  * dtitoditiw i  ^&*  bifisj, 
i  flMrit  f  aa  ^ ,  obtincttir  t  Btp  a  ^:aik  e.  ms. 

«|tt&ttttor«;it(J«)ds  prMnmi  bifim  i»  tiiti«|ic  «Ifi. 

mmfuidt  ^m  frmmu  fimdmtri  4mm4mmS 
ftmndlMtkH  «fmJm  kifit  tf  itihitudimt,  ^t 
"itm  eylinder  reAm  LM,  }neHn«tti«  MJT. 
tatrimqiit  b«fis  dtc«tnr  B  (J^.  73.).  Pimatt 
tyltndri  pcrpcndicnlcrti  premitur  'Mdtrti^ 
uu  dlfikjUtin^i^  f^ttt,  £ftvcr^gnK 
,tft«»  r«rp«air«  «d  «bfolatam,  ut  pl«nt  !«• 
clifMti  «lti|udo.«d  loiiginidiMf» ;  erg»  fi  ftra. 
«itat  «MUiiii  AuiU  cyiiiijjpv  M  i«  cmtwa 

dtc«^ 


'  '-'■ '  AIM  txHUmttir  ftidtculas  f Wtnehhret  flaidohijr 
iittfonqoc  dcn(braiQ  covRprifni  polTc;  i^qc  ifti  fttiliito^ 
explieim  ^ftahm  ^^mm  prdfioocifi  in  oinnll 
partct  {  cnfli  tnim  ecvpuf  pref!am  vfrqa  claflfca  lit 
«gar  m  omn^m  fiujim  ^equdtiter^  conftqai  d^cr'«l 
qaalsi  praflio  in  omncm  parremi  *  Fomin^  reficifli 
aere  torgidam ,  &  Yi&  aliqao  CKade  conclmm  ,.  vl 
mjlgna  tfomprimrs  niirctar  undtqQc  acr  pcmmipci^ 
daaftra  vafis ,  dt  «qHali  yfriom  qaantltarc  rcaget  fiv^ 
infundam  ,  (ive  in  Utcra  valit ,  (eu  dehiqoe  mCvaa* 
fix  illo  aotcm ,  qood  de  iphirra  aurea  pHns  mcmort* 
Jri,  onum  Htud  inferri  volunt ;  cofnprcflioncra  par'* 
tiom  ttqotdi  dcnfiorti  reUte^ad  noc  infcniibilem  cffi|f 

re  vera  tamcn  babcri. 

»        . 

Dcniquc  alii  fic  conflitoantt  Partca  pr^pri^l  9t' 
«lementaret  Aotdoram  denfiorom  durk  (ant »  dt  hi 
fompreffUesi  in  cirom  tamefi  intcrftitiis  refidcr  dul« 
dum  ifiqaod-iobtilittt  comprimi  potent  ^  qood  prcH^ 
liim*  vi  uia  claftica  reagit  in  omncm  (enfiim  ,  ficqiMl 
molccutat  elemcnraret  fluidi  denfioria  ^opcUit  in  ovnim 
Bem  partcm.        Non  rnale* 

Flotdam  qaoddam  (obtiltai  pofle  latifarc  in  in* 
terftitiit  Hquidi  dcnfioris  evincit  maetina  fneumaticar 
eonftituarar  in  ea  vu  aqaa  plenam ,  &  lofUbfia  repc* 
tjris  exhauriirur  aer  ;  conrinoo  balbr  aeris  anrea  in 
aquis  comprefiiy  |am  pondcrc  eeriff  (oocrioris  libcrati^ 
aquis  cgrediuncur  ,  ac  (bpernatwit.  Ergo  craifior  il« 
le  ter ,  qualcm  rc(piramQS  ^  penetrat ,  ac  replet  intcr* 
ftitla  ,  qus  inter  mokcalas  aqu«  intercedont.  Qoidl 
ni  interccdete  po(fi|  fluidum  atiqaod  aero  noftro  Gak% 
tiiios,  quod  intimc  aquam' pervadat ,  ^  ope  machi* 
nap  pneuinaricx  expelU  nen  poflit  ?  nam  acrciB  hono 
oCualem  ctiafTam  non  tffc  teqoalia  in  omnem  parteoi 
prtffionis  lubeiner  admittonr ,  caro  eadem  prtifio  ha« 
bcator  in  vHctf  B^hai^    Qold  OKnen  fi  in  ctoflt  fi( 

€c  }  •  fob« 


4»l       SfSiott.  opm  wn. 

fiMlifflfnQl  •€»»  fnalii  reippef  mtnee  In  meiHi  Btf- 
l^pne  poft  repeiifiis  otc»nqoc  fiiQioiies  ?  Qiii4  fi  fo«- 
^^  floidmn  «iiquod  fubtiliqs »  Hleni  pforfos  cfun  ««>, 

Sod  t  liqooribof  plcrisqQC  cfrtdicor  *  (bcqoc  ob&n- 
cfiicit,  ot  liqQidc  conleiccm  in  (olidc^  c»  o*  in 
ll^ciii »  qQod<|uc  iieruin  igmi ,  &  cciocis  •«fxtlto 
foimifl^  conglccistii  liqoorim  molccQlis  Auldicoio  n 
fc(&Cotc  ?  Ccrcc  tb  ciosmadi  Aoido  fiibttiiort,  &  ^U^ 
Jk94  pcnccrsri  Auidc  denfiorc  fttcdct  evspofctio  Uqoo- 
roin ,  c  c*  aqQ« ,  fi  cnim  cqoc  conftsre  ponctnr  pcr^ 
tiCQli«  folwn  durif ,  \f  minim  ^l^idi  ,  vik  patanc 
ficc  concipi  podc,  quomodo  fOolocQte  iftc  •  rciiflM 
^mflii  cvclUncor,  &  in  vsporcs  sbouic* 

Scd  cnim  :  nunquld  C$rtif/tanm  hsbebirur ,  qiric« 
fcis  fimiriam  Iwc  J^htikm  %i^c%  ?  Hcbcccur  li- 
CCC ;  babebirur  cb  iic  »  qui  (inccmai  oicteris?  iubeilic 
Csrtc  lan^  nocioncm  non  bsbcnc^  c  qQibQs  Csrriftcm  ' 
lisbciri  in  tsnca  lucc  PbiJo&phiff  Nmisoc*  AsxAssl- 
dfifki^  turiic  non  cft»  Mctcria  Sibfilis  CcrtcGi  dtn- 
iifliinc  c(t  \  ilU  s^modiim  fubtilii ,  ^serc  uruali  rcii 
rior,  Matcric  Carteiii  ubiquc  diffupditur  ,  pcr  tpft 
•dco  fpaiia  ccelcftis}  ifts  latcc  m  interftltUs  fluido* 
f  um ,  ^  forcc  Aprc  aor^fs  ctmQrphjrrsm  (  qocr  modl- 
cc  cft  alfitudo  rclccc  cd  fpaiic  ccelcitic)  clmtQr  <kci 

9f  2lS<  IhJIhuHs  kamgdnHi  qukfcnftihii 
finguls  iarizfltti4il(t  ahcHJtn  UmfU^  p4rM  4fV4li^ 
Hr  prmmt  in  mmm  jmfum  \  fa^  Qnim  :  gio^ 
l|Qiijic  cleer  fortius  promcc  aleoro  (ibi  conti* 
fluo »..  prt mee  eiin4em  pro  excc^Tu  ,%JtUim 
iucrum  )  prefTus  iTM^ni  fopfimct  «qualitcr 
(§t  4. )  J,  &,  «qucli;er  roprimot  oUfticiwf 
ftu  propria/ftu^alecrius  mcteri*  intor  ffuidQ» 
rum  nrcrfliciacompfehenf»!  f)UiB  eUfticitj^ 

agit 


'^  ^  o. 


Igtt  \n  ohHltm  parterh  ;^  «rgo.  IL ,  ^Hi  fiiif 
*p|F<r  drati  dtici)ja$  piirtes  undique  prement 
iri|i]9liter  ^  non  baberur  viriam  «quilibiltfig 
qua  fubUtf  mottttn  confeqat  neceno  eil  ver# 
lui  tam  perrem^  ubi  'minor  babetur  re^ 
{lentia  ;  ergo  nifi  molec^ly  omnes  prement 
«iqeHter^  fluide  non  quieftunt,  4^  ^ 

.  CoroU,  Incle  flaunt  (^ecntle  t  I*  liquidi  ImifQt 

gcfiei  parr^s  omnci  equilibriam  iervsMii  incer  ft*  U| 
tn  liqu  4it  vi  Ibltut  prcflionit  nalioi  unquARi  fnotiie 
iequUur;  com  enim  molccule  omnes  (ii^  in  •quiti* 
ht\t,  pre^Tiones  oppofitc,  omni  cs^  parre  l^uiici^ 
fe  fe  prprfai  ctldent ,  qoantumqdc  #li«  mQtuin  urg«» 
biint,  tantum  impcdicnt  elift.  IIL  Ad  motum  ii| 
liquido  ciendom  rcqotritor  vit  cliondc  provcnicot  ^ 
lofficit  dutcni  vii  minifni  i  i\xm  f qjti^rium  tpUat» 
«  • 

§,  «19.  SiHgftl^  $jusJim  firsH  parM  nm 
Pio40  prttfitmt  aqu4Uut  in  mmmpmfmr/id 
ip/f  fnmunuit  ^u^Utcr.  fr$b.  Obfer^pmtitfr 
fluiaa  (  pifi  odmodum  empla  fuerint;  f •  cf^ 
ifTgentti  lecus  i  aut  iTafta  maria  )  indnerv 
ftiperficiem  borizomi  parallelam  ;  ergo  fin« 
^nlis  partibus  ejiisdem  alfcujus  flratit  lea 
lamella^  incombunc  columnat  Ji^uales  $  babf^ 
turque  atqoaris  pitttum  premencium  nuipov' 
^us ;  ergo  finguUt  eiusdem  ftrati  partef  9^ 

Soa  iier  bremQnnir  •  cum  earondem  irimKI' 
dem  eue  debeaiK  effedus,       Confirm,   Sf 
ptures  tubi  ▼irrei  atrtnquo  aperti  gtqviit  pra^ 
ntnde  liquido  inmiorganmjr ,  ancirgtt  liquU 
diim  ad  oandem  in  fingalis  tubis  althodi^ 
^  C  c  4         *      iifm  I 


^      Mkn>  <i9m.m 


doram  p«rtes  in  ta<)«.T}  profhndiMt^  cxiwtfM' 
tef  ^fq^luer  pr,eini«  "  '    -  .     t  .>'  - 

pofdumi^fi.n  oinncfn  p^rccm  ;  tiCfp  n^  premunt  j|| 
•(iniem  jprteoi^     ^.   ninmtor  unicn  le  mpverc  iii; 
«mneiii  imS$m ,  %«  eK  catifle  daftkmtff  proftU^  &; 
VC  MifrMii  iiuiteritf  inrra  p^oroi  gfiBQrttin  hi#ei«A9>V 

Sd   ftlScit  «4  preflianetn  exeircndatn  in   omnem- 


He  Li^nf ^  yveniQn^  ex  c^infra  gravitatif ,  ^oc  |iem 

9j^,  niii  ftitenda  ilcQrfmn  «d,  vel  pr^p^  c^mnB 
^iiiviRi  Wgo  H()|i(€i44  nQn  pi^Qmunt^  nifi  dcQtTum^^ 
2«  ttiMnres  premtitiit  4-%  cnofla  ernvi^atit  |tr«i»4rio,  &^ 
r#Ar  &liep<  fitp9id^rkx  iiiium^  N,  h,  p<     E«t 
4mi  diftinQtone  M>fi>lvnnmr  reliquat  '  Mempe  •  gravit  > 
|aa«ft  rttip  pritnaria.  {k  ^ir^fft  cnr  Kqnoree  prc^ 
•llMit  l,anK{llai  in(criQre$  fibi  fuhi^idal  i  ^«oniam  v^^  ^ 
Mkiiuru  pr^i   nef<|nennt,  nHtli  it«g;«n|  fn  00111619 
finifli^i  ipA  li«e  fupei«iorom  LamcUarum  gravit^s  ctaR 
Si.^(K  f  4ic€P0  Iket , /iamdarfa ,  tmdm^i  V  m^0* 
##»  ^Or  ItquciromLanMU^inlertor^  peepiiaitt  \n  om^ 
Mih  («nruai.       CM%ri  ^<|oefiuKbnQdnm  floida  fieiBiifH 
4krio,  ^  in#ir^£|e  prmiaiic  aii^  c v  caufla  ^^  qotoi  ^ 
^ofTa  graviratis  I  ppQmcmt  enim  ei^  r^tian^  fiu  comn 
prefRonis.      JJtmi  J,  Repognat^  v^t  floiJa,  vj  graviratit 
Im  premant  ftirfiim,     Ija.  Ut  premant  (iirfom  dTrtft^ 
(e.printiiriai  C.  A.  reo«ndai}d,  IndheAe,  ac  me^iaAtQ  * 
viwniiBiBQncM  A«  «:  e.      P/«*^  II.  Si  Mv»»  p#^  * 
Hmnt  in  Qinnem  pirtoin  f-aherornim-^^ ,  opoi^teri  vil.^ 

ccrro  pre(foroQt  nutla  prorfiv:  mt  ^r^vitiia;  J?!,  Pf^p^& 

flwt  |r4vir«i  mlm  t^fCm  iu4it$Sk^f^-ViiiflXmi^*H^ 


y 


Qais  nmabQ  dtc«K;  pondcrjifl  4  j;nvit«(«ii)  A^i&Tiii^ 
mx  «o  ,  quod  ianci  uni  Hnpdiitmn  «ftolkt  panclat  mj« 

nus  4^  fksri  4t4iff£hiin?  i|ai^  iCftdiii  ppitei  41  $nty 

Upiciufii  .cubicorum  prefSotic  Cm  nm^  mo^uK  I^pide« 
Ini^riorcs  i 'ncc  igirqr  riiperioift  AsidoriHi  IphstrttUl 
«t rollunr  infniorcs.   q^*  N,  Cin bis (bUdii  obdflr  tna% 
jpr  refiCkeniis,  Ck  mioor  mobilitas,  <]ttdBi  tribui  deb«(* 
V^lidiori  pmiMip.  cohsiiaofi  &  figuriK  noii  fitis  ic«j«  * 
gsr^ ,  nigc  iphericir,  (fd  sngvlpte»  quc  incpttor  c^ 
«d  motnini^  proindf  n<m  C^ue    ftcilc  ciHrQdi,  vcl 
•ttolli  poiTunt ,  ut  i(pbxrttl«;      Ac  Aalejcnbt ,  fffx^ft 
X^xn  Oxm  mobilct  ttt  msximci  fk  cuivit  imprefiidiU^ 
^wilticnc  ccdunt,      Ut  SoUds  oibica ,  ^uirttfn  iinaiii' 
•Iteri  incuiubit ,  nm  iigunt  nifi  dirciSianf  vorticlii^'^ 
inare  «liorunt  grtriMl  <gui^«ntiam  ;  (jfbanfuiM  agiml^ 
f^cttiiduin  dirc^iunsoi  pundfnpi^  in  qt^iim  b«bietn« . 
inuiouf  eont^dm,      IMqut ;  fi  oorporc  (^lida  qoU  * 
4wi  t  ^  r>)ixi  iot  ^  ^  l^vktta  «crto  ordine  Qhi  ioH  * 
l^oncntnri  neripo^it^  nt  4^««  una  cUoMp  «ttoUitf«> 

|Vt  Ptrtet  llqttidi  ftiiida  contign«vin«g^prcnMu*; 
l^r ,  qucin  pitrtes  «  fixuda  mtgit  diftaotei  »,fra^  f^^^t 
les  Ucjuidoruin  liQn  prtmnutur  tqoalitcr,     ,  cWw% ' 
FUidorom.  partes  m  ««iffxi  cotumua  yntk^jU  fittt  noa'^ 

Jr^in^nuir  9qMaiit«r ;  iHsrigitar  fiuB  w  ttiifmL^mU 
u.  kmrfa^MtaU  t  feu  ilratp,      |t,  0.  t.  Non  nrCQ^vo»^ 
tof  f  quaiir^r  ti()uidoruin  pactct  in  diverfit  t«m^ti«^ 
Ht^^onraiibui  C.C,  :in  «tdcqi  Umcllai^  fiv«  ftti^a.  ^" 
Kt  Q.    Vid«  rationcm  pafirionit^  «  qoa  rqi«t«Rd%«Ap»'^ 
tclponfia  ttd  Onfim^ ;  mm  div«c%t  iiqnidacnm  mik^ 
m^  If^  ««d^  «olttOiM  fitia  tncttmbttn^  div«ifli  lH|«i« 
o^cttrn  altlcodmet,  atqne  «deo  pr^  m^wA  «UliadiMa*  . 

OiiiMtinm  MructtUcoia  iocnwiSlsQam  iMiktwiL. 


IN        sahU,^aifMtpft 


j0r  ^(ffoi"   III  Cdd^lli  ibltO  lCiCfll   lllWtlW  tm  f^ 


t »» 
f  «< 


'  .V.  IMAi  cf osdtfn  alcif QiJtnii  ir^titerlMipie. 
fDnnr  partcr  flM  fi^j^dl»!  tnm  pdh»  )N4cftf  4tiRi4f - 
lie  v^lidiQ^  preintt  M^revrinfi.  <|ciiiB  tqoa;  iralidi^t 
|fta7  (]^ain  %ltiiiif  ||e.  CK  A.  Ibida  ^effrtgme^^iliqtin 
fgant  fdiftrfe-  ^iritdtii  (pecilicir,  non  «^oiirfer  prr* 
iHiint  C  A»  t^mogf^a  N«  A.  4t  C«  Major  gfavitas  fpt- 
tiSca  pcndff 'a*  ittaibri  namero  tnolecQlarcim  corpui 
i4}tiodvtf  Jkii^00^em  iUiqu9  volufnlne  coii(lituentiQi|i|  <}Qf 
rnm  fingQl«  prfniQnr;  ae  proinde  fndobitatom  fS: 
inagis  premfre  corpora  (pedifce  graviorti  qufoi  le« 
f iora ,  6<i  t  fluldiT  lettftfinta  lum  c^nalitfr  pre mfre 
pnrtca  fiW  'fcb^cRlf  / 

VI,  Nfqof  flqldfl  fcwff^ief  cqof  alra  <;quatiter 
•ffmniK^  fQt'cerre  n^n  in  oifinbm  partem  seqQalirer 
prc»ili>ljf T  ergo.  Pr.  A.mkjbiP^efl: celerftas fluidornm 
ertimpcntiQm  e  ra(if  i)i  ftndo  *gerforatis ,  quam  in  !«• 
tere ,  (eo  fcframen  fKClfiitiir  in  Wdem  |  '(irf  in  diverfa 
C^mfimdo  altiindintf;  h.e.  citim  liquorfi  deduqnt  cfi- 
In  primo ,  nihim  i Ite A» ;  tnf  jori  anrem  <cleritati  re* 
fpondcre  dfPft  major  prf flio ,  ^uin  c (Tfftus  cauiBa  fiiif 
proporrloni^  edb  debcanr)  ergo.  Jjl.  Cttiui  liquo-. 
res  dcfl^nni  *afii  ^mo^fim  proprer  minprem  friftto- 
Wftn  C.  A.  proptcr  maJQrcin  prc(Boneni  Nt  A.  8t  G. 

^ftm  dMQmnlarf  ncqtTcb  P|iy(icoram  qoornndam 
0plnIoiicm,  Oc  in  his  pr^eipoc  Qaltemm.  Sic  fere 
{llii  Lainclla  {)ori?onr8lis  §b  (fig  67*)  non  premic 
Iftfraliter,  neque  nirfuni,  M  gravitate  fua  tantutii 
Wfmir  dfor(i;im,  J-aracHa  9  4  premitnr  a  (upcriorct« 
♦  ,  atqiif  phffhmfnifrMohtffi^txi\\xx\w\  furrQm  mo-^ 
40  >  (^d  ^  fatcralitfr,  Qt  denrfQm;  debrfuifi  tamfii 
|wnt?ftiam  tWadf  eaiiifii,  (AWctt  grtfviwh  fn<rr  S|- 
iniKeir  iNNHotht  f/dfor&m  j^cinir  dupUci  cx  cibini; 


Itttnlittr  foliini  «  cauflii  prfcmonti  limriorBm  Ut 
iii«UM:«i|lb  iodt  gcmiiM  foii&ci»fif.*  i.  li^idiKnm 
fvi^fimm  f$rt$udimmm  mfitrt  in  J^^  mmmkumt 
IM^ifr4/f»i««i,2,M>iy»te.i]iMrr  iUii  aiiftonbiitprtmt 
4(orruin  Utnrlto  «i  nt  t,  f  «^  oi  i,  f  /  of  9,  ftfi 
II.  PreffiQmm  h  AiMft ,  fHlfwrfim  undmm  fp  jiri» 
gfcfH  j»  eademfiri^mmr^rummmrMHmi  fid  mimm 
mmpmmMf  Jhffiend^  #  ^rr;  hiflc  prefiio  l«f«f«li»| 
Mi  ruritun  TfTfeiis  Uitieilc  4^  sOi  J4«m«ite  c4  m 
t|t/ai  )ff  ^9  }4lC«      Prain4c,  inqaiiint,  preft^ 

fmpndiailMrii  caltiscttny  e  bftfnclte-fnpcnir  pFcflHonem 

mr^lm  ponderc  «insdciii  Unnill^,  qiod  lamencrii 

)>«rf  txigniiin  iif  I  oc  infenfibilc  t^  ftmif 09999$  Lmriim 

f i^M  lifU^hrwm  9  finc  crreure  «fMroi  porcft,   kfHidg 

Stmmr^jmU^m  in  mnmtn  pmm ,  fi  prcflio  illa  trU 
nuitar^qibmricirCKwAii  lioriaoniatilKit^/^^acij«f/ipii»» 

hWvA  c^fiindum  c(lb  dc  toia  qnidiim  (liiidoffttiii 
iMilli  diftrtis  rcriiic  afiirment,  $ic  «rsuvnri  pcc^ 
l^cndicnlarit  prc(Kb  ouinslibft  horizQntatitliimeU^  (U* 
iptrcr  prodioncm  in  dinm  ftnfiim  pondcrc  iftiiii  t%ii 
mcU^t ;  «igo  componcndo  jNrcifioncc  QffiiM«m  imircri 
li  Uniclt^runi^  (ivc  toiint  ma9,prcffio  ptrpcndiciitf 
lcria  toiius  |i<]iiidi  iJipcrctiit  prctSoiicm  in  iliMHi  ftn» 


(umpra  I  non  dc  miirc  integrc ;  nc^  certom  iiabcnt  1 
pcrjkcndicniarcm  totioc  mad^  prciBoacm  pneYitcrc  frti 

^at  fir  in  alium  (cnfiim» 

liki  quidcm  ob)c<ilionc  hic  rccittra  nihil  orgcimf  | 
fd  ilftii  tioico,  vMerinti  <)ttl(i  rc(pondcinii 

VII,  Si  in  floidia  homogcncic  fiii)Qtt  iMiadtBl 
ff (f mdci  roajir  f rcOio ,  forcios  (rtmiMf  ikttii » i|it        ^ 

IWi  ^ 


Pr«  m.  Non  expmnior  flia}OiiK«ii4irficii2^trf«^in  cds» 
ceodki  fitah ,  qilc  profiinclt  0(}oig  toimcfgitur  ^-  qwm 
%«je»oiiniis  flltt»  At<{ai  veroK.«^rirl  .deborefnas.  t 
iftcat,  OKiQciduai  fitolaai  pirofondiaf  nicr&m  o 
do  ghieio  conftrido  cdaeta^oi^  *^tm  dom  minaf 
ppofiuidc  Ricr&oi ;  crgo*  |)|,  Sitiilt  profundforitat 
ffait  immtrfii  re  iffa  prcmitar'  mtgts;  qood^ttffittt 
ttm  cdoctMtcf  noo  mtiof  pondot  mi|fiit,  tr3>oi  dc* 
l»ct  «Aioni  colvmntnim  iat^rtliiM  i  &  tqnuum  ifiibr 
rtorum ,  <tatram  vU  umta  sBqoiliisritticm  iiidiiotrcQflK 
itlflmna  vcrticflitpt  :prtmemt»  Qood  dt  glaett  ingtb 
ilom.  tft  f '  fit  cxpcdio ;  cxpcrtmar  majorcm  diflScaktiF 
lcmi '.quia  pcncs  gltcttm ,  corpafQtiqucibliiloiii^-fKii)*! 
ccndt  fiiilt  validioret  limitcf  cohsfionif  ,  qimn>*«pcnft 

floifbi ,,  (|iiprain<ptncf  &ciIUmt '  (cptrtntar«    ;  > 

^\  \'^'\ 

%%2Q.  Buid^hommmAmnfriuimd^wtif 

iudmji  componmt  tj  ImUm^  ^*  P^jM^^*f^f%, 
nit^ti  piur^Um^  indmm. . '  Fr« '  r luidorQoi 
l|)bf!cul«  cuivis  imprefiioiit  proniilitiif  co^ 
(loalGls  urfftiH»0iriUiu  w  ttsque  deftflndttoc^ 
dttm  iflctti  'd^endofidi  altra  non  iit.^  E(l 
inro  ienipor  iocdt-  do(oendendf  iquoiifqi  in  ia« 
pOf6f i#  horironf i  ptnllohi  non-  fant ;  '^ergdt 
^inrquo  deilendonr^dum  fiht  in  fuper&cieS* 
ri^onn  paralloU»  fivo  W/Mm^  IL  Fingo. 
0<llumfum  aliauam  vtrticalem  s  x  altiorfpA. 
•Ilo  coliimna  ubi  vicina :  cotnprimoi ur  Cpbkm. 
inUf  f}ttid#m  colamnaB  ^x\  cumqae omnci 
^|u«dem  i»amoll«  partoi  a^quaiiter  premant in^ 
oninoro  Ifnfum^  «qualtror  iiidom  premetuo 
(^liaErttU  4^  ^q«  «d  in  f adcm  columna  boris^ 


^ 


.-*; 


MMiUi;  nlMlur!it4U]itt  globitlai  /fs  tfievil^t 
ia  OHmm^imrtittt»  cfttTiqiie  n{btl  impedbt 
mfmsCttt^um  (poniM^  Miiii  tibHMi  fiuidi 
pmmamM-^m  icicmiibtfe  )  .fttiitttttr-  ra^fMii 
fmmnfqmpmtm ^^hibtili  Irft ito aMkni  eo» 
Jttmna  vertiaili  emcipiemes ,  lec  pmmdmistb 
kliMui  tottc^  pefoeiidet  igimr  tkier^lQfmii 
A«:i  leplebitqoe  tocufli  celtdtltti  ab  ea»qiiMI 
^lojnoXafeendi&dtxtA  ^firmMr  tcototniiA 
qiiar¥is  altiof  auidlitriciMifJo&qQe  deftoii» 
<tit  eoQsqoe  I  deiii-cotum  Itquidum  i;om)tii#» 
ieat;  quiefcere  autem  notivpoteftj  nifi  iiii» 
gulatcaiumnc  finc  in  «quilibiicacei  i»ie«  9« 
earum  momentafintsqualia^  qucmomoMI^ 
f  um  aequalitas  obtinere  non  poteft  (pofita  Mi» 
tectriatam  homoMieitate)  difi[  cototitliit  fllil 
in  eadem  altimdmei  --  :^ 

'•?...•.  *i:t  1! 


n 


'  mi^n  tt%rtii  tdrtlbki  eetiimiitf  It^tarHM 

ipm^  irfnMMiur  attoHtrt  Victiuit«  IrHtat  iiit^  #ii|l 
tiHiii  ttt  i  tm  toRimtHt  Irltlntf  t^tltdetif  ituic  '{lirtfKti» 
tit  fpediee  I  tubetortitir  ttrtiifittiir  fti^H^ttig^  *M| 
fi  ntia,  vel  ^lerti  ^lainiis  ^kintis  di  umffa  (iant  #fa» 
Itfertif  Mgitfae  ^tiMitiiti  i>rtfiNint  yi€faiii«  etltihif 

^^ri^^^^^^h^^t^feA    ^Hi  i^^^i^^^^^^  ^^^^^B^^^^^^^  ^^i^A^^^Mi^^^ft    ^^^^^y^^^^^^^ 

ep^pmpmiB  1 9  levNiiip  eeieiiiinK  inefpaRE  1  j^enH^i 
iMccndeiit4  Uiee  tn  fwil  vela  OMria  itea|ieii|tii 
%tinciaai  horboori  pinlltlaei  y  (ed  cenriaiimi  ly 
lcei  aniin  £bi  depoftk  tate  grtriticis  1  ^M  idirfrfl 
ei  tn*  dtvrtfii  tttr*  lodt • 

M ,  K  cyltndri  ;  •iftrp*dMkm  *  ttttfiltiMtU» 
ifid4'tmboimtf^MntMJwhSmi'§n)ttthm  tom 


M  # 


|>rcffio  aniiti  ^  qoMi  flaiddtii  ^erctt  in  fim»  j 

tMi  ^mmMM)  ntimtt«'««<uninirism  fM^ 
«matmi  rahittrM  pofkft4i|ir  |  qcue  «tldciittr 
Imic  mimiro  eft  proporimmeif  ergo  pro(( 
fioin  fontfom  pender  i  bifli  k  ittirudtMli» 
qusdorunu  IL  InVitis tficlinitts liquidi pr#» 
iiunc  fundom  JkuSf^  fff  uu  gtMVtMi^fuB^ 
^  iutem  gfiviti^  tbfblmi  flaidt  homogoa^ 
•m  vohimen  i  five  roHditisyvoIumen  prifmi^ 
4it  iu<  ^Ufidri  ut  befiiduAi  in  iltimdioemi 
Ifgo^  piefio»  eft  .ttc  bifis  doAi  in  iltica* 
eiMem*' 


IrM^^  <2«Ui>P^iCI  B^k^  (:4<fimiflt  siitMi 

r&p  preffiotiet»  ^  dt  4  sltitoditiei  ^  Boii  bi&ft )  | 
i  flurit  0  si  ^  I  obtitiertir  i  Btps:  As  a^  h.  e.  itii« 

|tvjtor4ri(g:^{ds  ]iriiiititMt  baiim  i^  rstiiiite  ilti» 
10  i  «q^  ii^^&kM  ikimdioi  fimii|trcfr4iC|iftit 
Joiifftla  tedM  fsA. 


p     i* 


tKitai  cylintfer  r«ftai  iJITi  {neHn«flM  AfJT, 
litriMiqat  bafit  dtcitor  jB  (j^.  73.}.  Pandjtt 
tyiiftdrt  ptrpMdicttlarU  premicur  ivntgrta^ 

Uk.  tfjftlmitindi^  •(i6»&tm^  Eftvcrognt» 
,1ttt«i  fc^MAlya  ad  «bToliium.)  ut  pl<im  ii^ 
cbniti  «Itiiudtti^  longinidiiiiim » «rg*  ^  sra* 
.fiia^  iteitt  SoifU  cpfliiv  M  2«  cMfiim 


'    C3  x.fiees  x:B*t  MHs:  IM  i  MHV  proio. 
I  4«qu«  Mn  B  ¥t  M  ii  it*Ud  ta  ^B  m  iL  M- 

-..■.••••.•,•  iMN  ■■.>■-'  •"■■ 

«R  ^^M  LM  rM)4  ffgtti         -  *  » 

•  ..  .  •  .  ^».  ••         » 

tktidt  pyratnides »  ^h/<m  y&  pttmtntftuulm  « 
UM^uatn  /i  ln^  Ji^trtdt  tnfttUtrt  aauidij  fortU 
Nftn  tt  tit  Vi»  conieuiil }  cojus  bjdhi'itiptrlor 
inijof  fit  bfefi«rii  (jf^.  €9. )'  urgebitUt  !ft  «a 
fuhdta  dire^e  a  Mq  cylindro  dj  ^Ht^ 
qa»  mi(Sk"Jltt'C,  (^  BkA  Ofgebnfit  llit<rAt 
trgo  pr^ffio  in  fundnfii  «KMflMir  to  tt«M« 

200  C  bafii  fttperior  idf^inr  lirfw<ofi«i% 
ve>^ffi!>  fbrtt.»il18ai»l'«  '^ '  ■•  •     '  ' 


/ 


•^  fc 


IL  Sit  «II  edfitaim » eujdi  b«fi<  Inftrior 


fit  m;i)6r  ruptriore  (j%. 7Q«)t  deipdiiQrb pri 
fionefln  liiAdi  ia  vaTe  4£  CD  c^jMrt  «},  4|tu» 

b«ber«carumre^^«4  Co««pi«iiir«iiifli 
Ami^m  i A  «iMUii«i«»i  «odeai  MflipoM^ 
q^  littidam  in  v»(e  aaf pltori  d«Aif M(  fiihb  • 

du4i  fyktin  «odem  fcmpor*  confe^i  f xhib*p 
twac  4B«l«ri|«M«.  |*«rf«  «4  ,<«p«cH««-<yiitt» 
dri  i<>  Mii«ii»««p«cit«ti  «Imt^  4tjP.(««iaii 
#nidl  fli^a««'pritttcyitiMif«i  iH  ««littMitimH 
liRi  n  by^thfdc*min«f«r  iiiwwtHo  f f)| 
Mqajlttun  ititiM»  eylln^rt:^  b«(ei  fant  fttb 


-  ^lSo  iti  iilHhiShlctil  ra.    QtlaiVtiiVrimfffMPfii^CV 
jiiiiBiii iiihHiiiiiiii'|>irffiiiT"  ^' 


•  ilntlltMiMliimig^NDIPvfEtll, 


;Ati%$7<^amii)iMiif''^^ 


,  (iii)liiB'et<(X«A 

iljbili!  >'  &>°MiMH  «liWthvk 


.  Hrtbiw  ferpciKiiciiiarrttttt  iwttHnttb 

tk  )Ett«m  voiuttite  hltiSilc^  Vfi^  «Mfd  1\<lfiiliiil 
i^l^«iit;  €rg!6'.  Pr.  A.  Si  ttott  p^peiHtiiH,  ct  forlft 
tde^Attfia  jpreitittrd  noh  vid^Mf^  "q&fiA  tsArutti  firdflll 

,  <ii8Jil€iMr  a  lntetiW  tofli ;  ^  liis  vtirn  fcliliicti  m. 
ifuif  s  «^qgo^  P^-  «>•  L^tc^a  trotii  iUi^CRs  ftim  |)f Iffi  ii^ 
iclifiiMt  \  tt^vA  ifhi  ii<m  iuliiifrciift  t^ittHn  Ipmdw  Vtnrfo* 
ii't  tlf«o)nWfl<is ;  ti^Oi  ^.  -N.  A^«d  f;r.  CX  M.  ««» 
ttim  ^i^<6o  fijffinercru^  t  kmiWfi  <roni,  f?)ta^qtc# 
ifiielwirinii  tyliiiHiri  iWecili  C.  I^  ^ifipnm  «  kterilbusvob 
M  ^7.  M^  £c  IX V  &  Nr.  G.  |>MrtiW|fa  ytcrFbns  ttm^, 

^  {Uki-tiiii  «  eohsitmi^  mediis  riihi)«t^  f)^«i(rit>'ifqi»idi,<&» 
Ira  'e^rlirrdVttih  /^a  Bi  i^ni^mik  Vxohtllio  uftb^M^ 
tft«i  «hiMt<*  ««f»cdltn(kw 


\ 


Ui^  ^ihiiiiiidr  ti^g^  c^lMihiH  httinkl  fitto^ 
titfti;  «t^uc  it  iiftb^.*  mtdiantibtit  i&ittm  tffisjpiri^ 
Itotnt  fliftdum  VsXifi  tohfVis  ergo.  ]^.  b^.  Ii^.  JSi  ^ 
Kiin^j|«C€lraits  ibe{)tnt)  aot  hifi  prdflioht  tvik  ige^ 
^ht  th  hritdiH  ^  cotumhs  ihtdiir  ft  ft  «tl  jattrt  dil^ 
Ihndtirtht;  hhnt  Vtrt>  hiAitn  mcrditiruhi  pcenit^ht  ^fhlt 
thftr^eht^Ut^rtlt&^  i)cqti6  Victs  t>betnit  lictrhh)  fbliftii^ 
J^^i  jflulbi^jccdiijslprtthr  diifFuiio  mtditirhhi.  iScdltk 
«t^  &iida  ^olS  Wgeht*  pt^mbiithi  tck  fihvdhlh^  lAiitt 
^lciir.i^hhinff  ktttiielk  V' 


♦  .t 


tV.  kh  Vtft  ^nito  fhjp^rUrcb^^^  ^^.  7^*) 

liMik  ifit  ttdtin  prtflib  ^  i^h^  iii  cyluidnth  e^h^thl 
l»HSi  & airitui^inii,;  ^rgd..  lE^h  A..boVumh« JlareH;» 
its  Vaiia  itohici  bitviorts  fuht  tohtmhii  tjj^lindHci  s  tfl^ 
Ims  icilqvt  funiium  ^rehiunt  |  trgi^.  tjt»  iBitvioiiitt 
fiiril »  «Oftti^Qhieaiar  hirtiigtl  iUis  dideh)  pttilito )  ^^ 
tiabtchr  in  quacyh<}cie  colhmua  iiccbhqUt  lohg*  @»  A» 
titti  ttfmJhtuiJiGaihir  N|  A*  &  C.    Singula  cju^tih  t^ii 


•■at^diA^iitiiflM  «iisieitf  «dNifttantcttiibfc<V}ciMld*HIRMc 
)ffi^^nai'prenftiHefiMa«itni  -^«fMW  |^ei  ^fim  i 

iRAt1in"«ati^  ''I.AIntHli-liorrzontiiif  "eaiH'  ^^i^dKMt 

'ii.^efR'^."  si  (Mtiitihtt  ^n^m  amm  cputm»^ 

^Umi  itti^  ^tttit^t  bfevibfesi^^  qtniMgl4>M|9Mii, 
'«flAi  0rMiaat'ghiriMi<  iHtnHiitt  ^lriilpm  ^  At  'liqt^ 
•mU^^ifbWi^ay')  <fMt«irar6:)mmiin{i!ah«  etAifiSHd)^ 
*!>)&',  4qUt^tMti^¥briiVibrek,'  tt-itf^ordfl^Mmt-, 
%iJ!a'diH«i^  mMtfi^tilc  In  €oiem  ftmo  %iiid»m  edta» 
•5»eflli4a«irt'r8eH|iit*=a*«(nt;  '  -    '•     '"^  •"  ">  '" 

•^>|  itfiii^ijnl»    io      w    iMi.'j.-.  »        .1,   .  .»1  ,'11   ••brij^ 

'    t  ^Vi^Qtfi'W««i>  <Bftiriet\nb<la"feai*>iW  f illr»g»Bi». 

'ViidAi "i ^  airilUJiUeiin'  HiAih^i  ;'1ion'(eflm'9iMnf 'ptth. 
dnt ,  eaniesiqae  prtflionem  ;  atquf  liititSile  *dMteM(;^ 

tSo  dKmamJia  ilt  ex  bali  duflyi  in  alrituclinein  ;  er> 
■■^X  V"^- M''^^  lttidtMde«->^ni^ut<ol{  funA 
iftdbHi  Atetti  e.  IM.  olf  vaiidiorMn  altet^tft  fiMI 
'*ftMyiiMieiti'N.'  Mi  fic  ]>.'ni.  Qt  'N;iCi  <Qtii  «tftimk 
<'<n6  fcdtii£&m '^)ut  fiiMiw(if}hiMa(i(Ks^Jafflh«i««^ 
'^'hmk''0i}\  ob  af^ifllttiiiliij'  iJdliiHtoneA  {^tiiS^y 
lltinrV;  itMin  foitit^  di;bet''nr«inofieill  tmMiflit 
^crptftidibQl^rein  ,'  {tl^eraldtti!,  i^iii"dc'iiMAm  jikh- 
haaiiia  ditie^Buidam,  'fifiAa^mfeae^fiftMtWtMa 
iUc^,''  ¥kc  WM,  '^a>fednS  fe^''(Kto«>ii/iM», 
Vmikki^i  Vlibiirai  i  Vai  •  aUtilia^<likliiMibat«tik%H' 
^iKinlf  ;''lidW«rqt(e  fiiiMtiin  «tobileiii";  4it(^<«it ««« 
fbftineatnr,  cedat  pr«(B9iiI'irqaiA ^iixtiMM^plMfieAo 
.  Mm  non  majarem  «dlubcnda^  ^e  (uilinendo ,  vel  «f* 
"Idil^O^^fiii^lfafiVt^rdl  di])iUi3'mliiRJricJii|6ltqoC 


N 


,1fWW:$««E^  -WIW)  PfJndtt^  $^(|m« s^  fJ"««9W»,  /«««F»  nT 

;iHitturt.4i<ioa  :p|cw  i?i:sfy^?fP*ff5BfPWqi^ffi8ir;«^ 
-  fit  cpnrra  tuiKkin  vaiis  ob  ^ol)irr«ntwa|<j  ifyi^f^  qun 
faado  immobiU.  Ccter^iin  vis,  ^  efficacitis  prth 
^  m»i|cmnH  iHmAoA"!^^  ^^^^  coni^o ^convergepte  ucii 
jf »»loraw??  fi4^fndp^,  Wt  iisvai^o  Aio^in  mobilitip^ 
4|^fthiftftiim«rf,,^t  jl^^iwr  i^f fctQHi»,ip  . Ad'4t^^ 

l^Wtef«>  fif^<5ritatc)pc^flji^r«^,d^c5pfiqfjidi^n^e  fi^  . 

-*^fWjqfft2JHfJMHWr,?,f^«8!  ^995$co^.|aWH!9  ffi^ 

br».*  Asr.o[»flfJ!r»qr^l4«miEr4i/i(fJn(|gprihi\^^ 
'  ^ipfAWft  WWftHfn^  (^^»*' <^*  Mi:,aiii$.ipia»nt%^|Sr. 
^JK.m/&W^I?»«J»S»9^i^"9^«^ttS;al>  efBuxo  ifcdiQito.Cf. 

^i^^hm^^^mfWm ^Cf  conico,  auandoqui^^mi^ 
n^rtifWii^.Wlftlpti^^i^^^-flWMP  iw^t.d(Bb€i  jnt(j|l|k 

iMip9Rmn§f  P«;f%faf4  w^  l^dJBkM^c^onfifl^^ 

jc  (jV  .  obitsri.ifiiii  •7i)d.rtJjihr3'iiii'ii*,  in  »11;»  . ;  -nfc  .  -•/ia 


AtqH  tmca  cspcriauia  mtOB  cBi 


m  teoisorc 

|PIVplUCl 


qaann 


mtdnpk  iit ;  prmide  eflrednf  cft  proportioiC 
Mmi  qoMfarapfar.      Eoinnrero  fi  dimlLtflaK 


notiu  non  oiinas  eonfideranda  ef 
fitM ,  qnonuD  aittnfn  altero  conipail 


CtJ3  WWl"'^4^rf  «irjugiiilie  msnibuihlfi  nidf> 

£lehiTiiO|»&  eOflflQUllKmtltlkuS^tn 

oup».i8,iIqmB  snpa  luincnoq  iduJ  moD  tmm 

>fii$8l«4S}iSlif)jsrlt»|)Mt^ti«^^iMii^ 

flfukiteaii,  KlttH«trtei<miflMWi>,  ifei  IWAAAI^," 

sTi  '  £  ba 


Dfmthifiildoiruii  .     .    ^r^ 
«ffigns»  ■'"4'wteftwiM  criWl%emh"jlW 

%^MnM](,-ino(ioiqib  BtifDj^fbslxiia-iq  ;  ifl  Bl(|int(;tip 
■     '   "   tnsydiiiiS        .^iqoibeop  ino3 

'  .|,i;.,iLu;"!.-,i;:3  ?unmi  fion-zjnom 

-fl»Wi_!i4fU:|:iif.':  yia.:.^  rT-(j:&!;.9  moMup  .g^Ai 
$.  32^.  In  fuhit  ammuKieMtttfut  (eu  reouJ 


/i&ii^'«}iriWriiiim"''P«rit*>ii«te'bsal4sil'*- 


ui  «qultibrio.  Pr.  H,S  «*  aSB  «tp»*»» 
Ifra  I  Cr  ijuiJim  luminii ,  lique  nMlOa  ad  eaar; 
dem  sltitudipem  afliirffunt,  ha)>etup-^  OsS; 
mNU(ik(l«btalIfIWM)nl  aiMiKi  ntafi.' 
nim,  cum  tubi  ponanturzque  amplii&teqns, 
«ltt<it<«iB!b«6^)i«4««»wi(^it>f«»le^t».. 
tiuw  ift«  •niiprliiyuituimjitft  altetuanmfatit 
4ll^mijlUiiit)Mi#itttwi,Milii)d(i  'i«  ifu^iilaiiki 
tiMttt&itgOWIialtiiMliAnkMtteirpnisB» 
d((Pnflwpl»«(i«n»^f  ?fc!?«>*<iwi»j  ,er»& 
Uii>KM«t|fM*l«l>&in^<M>Miiiikahem>  agj) 
oHjKMai  wtn  ii)«niilft»ii«»«o|»lilie»«>«r^ 
MAMItil  l^  ,tMt«i<l«li«i<«ttrii>i  ^ndduis 


'*  (ti*^u  Af:  «I  rS  <  1 C5,  fif  que  defedui  mtl^t 
Dd  3  •         f« 


'^ 


jjfe  ^''•'^(•nijrto  «Tlufij   ,ifif)'  Twk>  v{f'/ti  •    TriLPii 
i^  oml  'i^riini  ^  ifjo;  ij.fnnu  'jfc    ifrrjifj^qfni  cnt>niw 


««««•teftl  '•  ^Vi^iNjai' 6&hdiiW  Itawdf» 


•^etndem  altiwlhsrrif ''flfbrgere  «iibenf.      ^xcipti 


cqitii  longioru.      N«n  fi  CTM  lUud  Drevira^tfqariih 

Irtiih  tfihii-oflleiat ,  qua  fWmiaJi9i|aarttJ«difeafi<toi^ 
«ttituditi«lii^i(fi«rgai|jpJi4M}4ft  W^b4(*i»,f,lHiD|(Eiii^ 

|ienti(iari  fciltcer:  aerivantar  aqufPclaco  uiqt^Qjiw 
«elfiore  per  oiMlemfiibterrHictiini-qiKnibiBdci.^^ 
Sjw«4<#W*nt*jr  MU^  ftUcn^ep,  jfeMrYi^  ^iturf 

itiiunr,  a  qaa  proicct<e  lunt,  multa  ^"^i!i^i^^U$  JbfRA 
dihem  impediant,  ac  itniiiinauitt ;  mtfiuit  inii^refiS 


!?£hiiM;i^  h4llir^if«^i|  Vl»MmtlMtHH^^ 

1$ /It^l^ifif  ikooiincittccp»^^ 
tus,  inftar  tuborttm  cmnmunicamium  pp9iiififio%^ildcp« 
rhrata  ad  candcnt  altitodincm  afTurgcire  potcrit ,  nb} 
istftigiHt{tfesctUt^)&a»i9hpfe^t|d9<<pr^^  ' 

2*©qi3x3    '    iinodob  3'f'jo'irtIU    •? -•.!••.  k.:.^   <iitr^  f:*;* 

uui  fpeeifica.      FiogVfemhi^ffigUrdW  UMgim^ 
replerj  tabos  ejusd^m  luminis..tnnuibuimo« 

Qi^  Dd  4  «        altu 


4«%  jHNvflAttlMPMR 


fartorej  prtonde  ad  Abcm«iWAm)L»ifMA^'lttf 
^cim  .cquaUtfteiii  haiberi  debet  major  aUku< 


Ocm  in*ior|  tjito  {na|or  ett  gravitas  Ipecinca 


'V*  "-'''^\  -    -  ^     ■  . 


CAininuni«ant)bt)s  coiiquicicanf,  debent  eorum  «Ititii*  ' 


"jhju  loitai  J3{jt)b  iwdefi  insjsTilujjjs  rni.t 


t^taMrwDtmyM^Wdnttfy^ft  ^fufacrpcun»  wl 


d«ni«r^tt«re  dclKMt  ^(«xtMiiniinA<  ji|u«Mit**(| 

brium  Inter  columaam  conflanttfhi^^eX  SquHL^.'* 
-^&bejrp  |,i9K^4At9«  ^Mffn^il!»t?fl»l9i,.,^o     -' 


1 


j 


} .  s^iiw^nwJiim^mttM^syq""!" 


lllWI9f{J|i;>9LC  I  ^<>*>n  denliQre,  li  utrinine  aondos  ^> 

J^ut<'il'gUa>'f</iMv  <iU«>£niSri9'  aimm 

qMKbr*t^:''>nfli4fie-cTUm«oi(i«ln«  tbbdaf^ufttfiMaV 
Mi:<1U)tfibfre,  aqiilifasauiefit  liAat  MivnHTfltnan 

•<<»Hlim'.'<lffl9»in  ("liei-j  !""("'n<lenv4ei5tef„i^, 

^4  <l^)tt;<ie  liquiilo  tvriQre,  qu>m.acnriirrc«'  nmcf 

'nfiriiiiCtis  jrollttd-gieilf  Cdidsta  AicKc^IvrW 

iTnfmrfr  „liAn  sSlSi^."  ■■■■  '    fl-    ,  'oi''»! 


■■•^n  ;■-:  i.i^j  ■■^.[.■■^■^  :::■!. p  ,iijL[iOil 

«•tUfWA  t«n^(ni  JifiitUii  ^idunKJ^^^fihb 
ftprtm*  ft  tomfsnxt  ad  lAtUtm^^&Aiglii'^\Mt 
tolum  liqmda  immirfum  ^irjifttt  la  Uto  ,  ^uo  tnf- 

»fiawrf.i'1Po&i»no  |WiT£lni* 
rm*    i>riil>;ipiiis  Ilii'  <Ul 
Irqutdj 
lii-ail^ 

sjlisdci 

qinpfj.iDfgOr  ili  Idepi 
folido'-«itisdein  gfsvihii 
<H  li(}eMii'j'  fea  qoievU 

«wtjhi^,Xol)((swi,j(4t» 
iiiii»;t*uBti  jiiuieifiin,  c 
con4in«tur„ 


Wli 


*» 


Utvrokflliuolli  f  -  ip&d^tnfc4wilH)4erQ,4«l)Mp 
Gi)«nqi»«,«j'  foMuRi^iniiKiifufiin.  ^  TiJfcirtMu* 
iiYiWftfftift-eft-iBals-ii  itftwrprwrilewpMjA* 

levior  ,  nihiIotninus.ftaBC5.i«9|fq!tHRtf<yft«fe 
pondut,  quod  prxTilet  ponaefi  /ijii^i  parif, 

difi^a^rotyi^  <Uid^  utqlm^tfi  dbladlinii 

4«iiifilM*Abew«''.>.''';   '.>  i...<-i,--i  >\  v.».>-.'',,i\ 

-mi  Qiit.  ,  o^oi  ua  li'.l',  ;i^,  .„,i' ,.,«,'..i'i  .li.m^i'  nuij„l 


""Isaui'  ^ilil«'congi!«,"«lti««i»A  ocj«l»«i«^ 
nnli  Mi^raiBqpbso»iientt«]a;xi:  .|.  yVdRffiwi^iwnlt 
<»*9  Wpwirf>W»ffii:r-#i^iw>WWB-Wii»Hyjifett 
"Wftific^aisiiSHinwiM.  mi^imtoiilfeWfi 

qilu!e  ^*cr relSU  id  am»l  mannM  funi  Jpcrtfrce  14- 

;5!S?i34vaiM«t  f  tkt»'  .j  >M««iaw 


nsbcibiilsbirBlaM  ba^v^  iotf ortQDHIiiiilt  Kmp 


iviii  «if  «HiSi.„ 
oia'iII!c«Hi»iir.''"''l£  flvirt-ei^ltmi^iilfillV'^' 
«>tipii«lfl«i  lMt««:&4l)it<8U<;  i1ll|;'ellniadi<ak 

■j  ..,  .;-««tl»...i> 


«>»       smfi>'ii0fi^ 


■jljlill*  "«llli 

■•kifiWI»»» 
^V*  MII7 
4Kll^lAM»Ji  la' 
WtriaMdb"l<li|l 
*8il»edi»^igiM'' 
twniscjiliiiaci' 

f«'WfittrtftVfltei 
**"*  M*fi« 

p*«'"iii  'tinsi 
«intiebatprtllidri 

CfMfitii  ftBulte 
•«i«ISI»iti}u6lt| 
^n^tilttsiitintllM 

«"ititjjwKrtfe 
"•»'i|vliiw(i»IR« 

JwnWpjiiflli  pt, 
nWiriimnj«»« , 
'^(i«w[tii'@^ 
<i  op?  vcUctr  fi« 
•ft  pnp  aiiii»  volu 
<Mtn'i«ariiAii 


^iliuq 


ilJ*  'SirolllllM   cum  ffltel;,fc[i!,  iiilsw,,.*""»» 

€SW?f«»L  !!#**W.  «1"0»R™  ■?'«'."«,"• 

ffiSS.TSi,T>Sa 'fia  jBWfWiJi'1'W*  'l«WIW.i!'«»« 

"SkWss?  t,  j'?''5'¥  ,«#'«;?.'«"!«'  'fcifiOT* 

'•iKSlS  !,i,f'%'''''W'|(HiJ'H«!'V'''»»*i'«*""* 
dflfiimUWTMmBiSim^^riijfii^lio^f  oimMhrqtHwonlav 

iK?ifcriWi™j;&'*l^,jro'i*j'i=,':Misw''e*>* 

^lr  ^ym0'  *«««"ff.iffl/'*»'H«';l««'W  , 
alf^il»  la<W!»ir,yi(,  <m™,,,,<(jw(m;,j>ivS»  iii,<»h 

immw:msmt>^  n<i«i 

'=T!M  «fS»*,Jll'»«l*«|i«i 
W^;i  .1?'W^'5'«l"'''<*»I 

,^lQm,^e,lfflil''wft,Nia»  fe 
p»ffl'p''q''*ip>i»'w«'».,fi»** 

l5..*W|.»l»i)-*«r'W»«' 
m,s'fm^:imfminmiir*a 

m.JWiH™!  «IlWiffitMl 

!«»«W?i.,  »l»ii))w»i*»" 
c«>i9M:#l«lW'mi'.lw> 

i>iim'i,,<li,^<l,i,<pmiiri'«  >«  Mifft^stKiMl'^' 
S»T>dwi».i<niim«MA><.)««^rl!mi'WWi&iffi! 


«ur;  Oiniiiter  ergo  (blidani  ve^^flkttPf  «tl 

^(^^ip0y|    k\vyj;^ivr    jo..\v.»4'|     aVc--.   ■.  •  .    u\i*\i^   4»'   ;=*- - 

^liniirfi  tiU|^irtjp  mwtttsof  i^  idiicrf  priort^ocftidrittin 

^l^eriMeriiipteiM;'^  ^fn^^^  «xf  JMdein '  lAktidi  bptrliio 

iiitfp«6ilaiusi^Tjkftf  yti^t  ibih^  dc|Mnifasac 

,  ^*><$riiic  «qtniKKi  ^0(lihicftittiin^:t«l'ttqtiilt)>rHim  cnm 

^^fdnd^BJHiS<^4iliferpijbilMci  Imslnp  «diieteniiis.      M* 

^iriifti  'dciniAt  ii^  ftimneigicu|C  toiMiiijiHi^er  icrfi* 

nte';'?tdibls  /««ribiffc  trqui^riuWt^^  prdi^ondefare 

«  Nwnmi  foHdtiibui  HDipftitn^  q  Cy^linidruni  civQni  ri- 

^-«pleop/afvi ;  fitettcr  t^tnitr^iWititii  v^  niantfed^ 

cfsndieicr  p9ndut'i^oii  cttrittttni' iibltn-itocplcntti  »  le 

i^yrottide,  volttmini  ^yiindrf  ib)idi<re^ondehtii  cqairi 

afitndv^  fod€i|t  ftttdo  intrt  tqidim.ti^  U, 

ri^lindtD^  vitrct^td&ininiticet»  urqneiftqajrr  rcfAttii 

I  itetnittittir  gtobtilQs  cetfiit »  qui  (peciiiot 'Jtvior  co^ 

M%  ^^«mr 'innttsbir^,:  ptrtem  rtinen  illiiiiiexrrndet» 

9M«  Mbbt^^^^  ^iidtcri«MMlii0i 

4 


pellic  ;   catnqae  (itjb  eo4em  vplQminc  majus  (ic  poq* 

tarpor^  iiverfa  gravitatis  ^tcipcdi  invicttn   Cfni^f^ 
n»  ,  nams  fmdnis^^tti  vidibimr^  fwl  fuk  eodath 
mhmiimjpi^  pmJnmi.mm^rqwAdliitQ^ 
»«|ftpf^aBipqUttdb  iltnnM^  iMam^4>^4tifle2gtiiinii|nfllMri 
atHMaptBfoMdoi  if  qiiiHlwriityiiuiieftfiii».  ^:^q^  paUm^ 
ocitiatft  ^im&jH  vcrfiteen:^  «ai-^Mrii^ar^fAnd^iid^ 
ttAiyiMiieryvohBwetti  fwmtidBk3Biqnz,ik  ittptdi  ftbBoi|dcit 
rmDunoibdinqiftUwelMqi^iii^  W^  ^iiiptroiifti^gtmi  ; 
>^ia   «ibQiibif&booiqatl  imittiRlBr^:fiM2»4il^^ 
TqdamjbcgBiictHWttt  opelytKriaPf  icffi  MkM#nAiitMC 
^«ftKii^rrqqetirf  fl%^';^dqoiro  thacimiitideliiivojmriia 
^tdtjde  locaihfiri-^^fy^teUit  tMii  waipjkbolfbmmaA  ^ 
r>^tiim  nrgem  ii  i^i  flti  fqnea .  ttbtajjtqftff»  m  ^  ««^oor  jkf^ 
^/ideris  miit^(«idi2)kqrJittnim*^-  Mitit  ^  fcmioii^iitiff» 
)  ^ciirgenti^fimi&^enM-aqtiiflirftqtiilibrentQr  ^^knoiifKi 
tb  iqdirilKtmmiflilptoytttir  wmAihatktin^yj^jp^^ 
op^nXfitiiMnai^i^  HttiBsi^dmniib^tiaiifio  Annli^i 
ff]iatci^)^«ie6oB«fmot^l|  «u^tByitriiiitoi^KtiinfifilrFateeri 
^  cadivif  vjn  ^ttt'iUf«irmdiii^«  f^^i«htm,imekifiiitr^?jb 

^j^K  •        FrobL 


•   •^^■^■^        ^^^^^^»      ^vW^MW    ^W9      ^BWy  w   ■      ^t^    \ 

Sit  pondds  imfBc  inicre  pcMdmi*  s:  t0&  tibr«  s:  nI^ 
Sit  ptMidui  eitisdeAi  imffie  i)i  iqtt  Kbritr  m  99%  iflitv 
is  «•  Qtointfm  itleognit*  «liri  !n  niAifii  faMitis  ditigKor 
C!  ir.  Argenti  ^  >.  Qata  jptms  ftnnl  (im/fltt  «t^ 
#qtiinl  toton ,  fitt  «  i|»  jr  :«  mi  ;  prmtidc^u»  t  jf- 
m  m  m,  x^  Jartt  qticnittir  qMltMi  pokidcril  ilk 
uqt»  ftmiiterc  vidcaciir  iifNlun  ^  poftcc  «orftlitMi  iil 
«lixto  lctdilSi.  Sic  rcpcrics  1  cipc  miiflaM  «Qffi  fini  kk 
•crc  pnndcrttl  3  19^  libr.  >  dcpttbtndts  tiiidcwi  in 
^na  appdidcre  18.  lfl^«     Itcfnm  tkpt  muitkm  vt^ 

rnti  pctfi )  cn^iis  pondns  cxtra  aquas  m  i^.  Vk^  \ 
aqOia  tnnldabitur  dccima  fni  partt ,  Ik  ipptmitt 
9«  lil>r»  Incatur  tandcm  iMet  ptoportio  r  tf.  Marft 
nuri  pnri  cktra  a^qnas  pon<ierati  appthdokit  iB^tfbraOt 
Jacogniift  maira  fiari  in  mixto  lattntiii  qoantoni  ifi  ^ 

tj# 
msM  «pptodtt  f    Sivti  t)  I  t|  is  dr  t  "««^  (Mft 

ttiiffi  tft  4tos  ttrm(0M  6^  proportioiMilit )  v    Edkni 
incthodo  opcrabcrfa  droa  crgcncam  ^  ficcqut  l  ik  l  | 

9iii*9* 

Qoait  <fsf^  fm  a  f  l^  l^ 


rtdlittil 


)» 


I» 

Ifo  a  i^  •  ^  t?t  fMi 

DL  •  «  (190  s  ••  t7t  «)  t  >  li  )6^ 


mhmiffk jit^i»^-      m^ 


^^MH^m^fafidamfm  attsl|ntfiHB!irtMj^  iMflfe^tf  M 
-mnt  *-.  z'>:r9i«I  ^tm  m  hat^  mlngt>:ii^Jfwthnm^  •«  :;=i 

m   li-ijhm^  ii»»l*t«0D  imriiBifp  tp.-i]^      Jb)68  *«  >» 
h^ii>iiiiiiijtttqta<ofcl?ttb»toft  Mtriiwtei  fTMtrrrfnid|ll 

ium  mq^tdehifttrf   4tbet^  quahtuinvis  ctJim  dorptof 
lMbiK3mi»ttfiMft>iiM|0^  WM 

dos   omliei  Vi   ergo  pDndcri%Hj^fiid^  ^imdum   petlt* 

^iV«>-  «n<OT  j  V«m  fuprenUL   ^us  fygerfictes  fit  tn  iiM4 
tadt.n  bori%oniaU  cmnfluidv;    dt  cijl^^  (« iftj/ww-^^Vf |t 

uqitas  vi  ttJ^A^iiMymfnj^^nUiiz^iA^ 

^U9  confiuuetUr,       b^einpe  i  fondliin  qj^sdcm  graV^ 
tif  fpcciRc«  cum  fluidjl  epdem  platic  taa|)o  fc  IjibSr* 
aebet.  quofluidi  qi^^pottio  fijb  ffaR  V^lli^mff*;^ 
itqoi  ifta  fe  cotiipoliirariiBSli!bfeir5^  ^P^J^^ 
fieics  in  cadem  linea  hdffjtontali  cum  alfls  flaidl^r» . 


fieics  in  cadem  linea  hdtT^ontah  curti  ains  nawitTfir» . 
tlonibtijSftte  do^mcunque  locutti  occupiveHti  liTiiiiOU 

tjff  iftirrHittTitt»  lc#  *^mm  ^artim**#t<iteitlt 

irtdocreffctotte  ideo  ti>tom  mcrgi  debet  j  i|^nd*  au* 
tem  pfotwndlus  ihcirfiaiii  qodflk  KA  Ctrti^liRifct»»  Wl 
CorfU4  Jf^ttd^t^t  t^ifl  ^'^^^i^l^^jf/Ml 


^    4)4  St^  tU  dfun 

fimJii  ixptlfi  ad^iput  p0tA$$  toHUtfiliiB ;  f(  eiiint  M« 
mifii  fluidi  pottio  adffqoabit  potidiis  totios  (blidf^  jant 
colttmiM  iila  conftatis  «  ilnido  ,  6c  &lido  ifnpofito  erif 
jn  «eqttilibiHo ;  (blidiwtl  trgo  iiiftitMri  ^  &  «b  iiiieriorl 
defi:«n(a  arceri  debet^ 

CordU.  ItU  BdiidUi  A  filid4  mnijfum  aier/fiit  gto^ 
^itati  fiuidi ;  pars  enim  ponderis  ^  quam  (bltdum  itl 
j9tiido  amifit ,  faftetitatiirj  obitqge  vices  floidi  ei^polfl  } 
proinde  inftar  flnidi  expulfipremerei  ac  gravitare  de« 
bet  eom  reliquo  fiaidoi 

Schl.  It   Rei  iltQfttatid»  perqtiailt   ticeottiitiO< 
4tim  experimeittntn  recitat  P.  Mako ;    (ic  iile  i   Vui 
vitreum  4qua  fifi^  ixplenm  e  hilaUtt  fii/pefidituf  ^  tis 
qUi  immergitUr  eyliuder  ^eus  di  drhie  equiut  i  aijUs 
axtrermm  clavo  fixuni  fa  |   depeiidei^S ,  iteque  fmdum  ^  * 
mt  latera  aafis  couthigens  :  intpofito  deinde  iu  laudent 
cppofitam  fondere  dd  aquilihritaten^  omnia  tedueUntur* 
JEbctrado  cyliudlro  iUito  deftruittir  ttqUilibritas»      RepO»^ 
ratitt  autem ,  fi  aqUa'  ejusdem  cum  cylindro  ifdiumiuis 
tU  tas  affundatur.       Unde  per/picue  inteUigitur  eduSa 
cylindro  tantUm  ponderis  adefttptum  fUiJfe  aqitit ,  ^Ott» 
tum  is  iti  eadem  petdiderdti      Hinc  porro  facile  erui* 
tUr  mitabiUs  cujuspiam  plnenorHeni  ratio  i  fi  lauci  lihr^i 
infifiat  cylinder  loiigus  aqUa  teptetUSy  cujus  fittntfia  fu* 
ferficiei  intemrfus  fit  ghbus  plumheUs  ieitui  filo  bracbio ' 
lihrdt  affixus  ^  ae  ponderihUs  in   lancefn  altertitrafft  itrt* 
fOfitis  plend  prociiretnt  aqltilibtitas  ;  ambufto  fih  ^  V  ' 
globo  pet  aquam  detabente  lanX  iUa  attoUitut.     At  poft^ 
quam  globtiS  ad  fiindttm  devenieuS  conquicverit ,  redii ' 
prifliua  aquilibtitas*     Sit  eiiim  poudus  aqud  ^  ac  q^liipk 
drifirrtul  :tj  F,  pondus  globi  t^  G^  pOitdUs  aqU^i  ejusdettt 
votttminis  zsg  ^  perdet  globttS  de  fuo  pouderi  pattemg 
accrefcentetn  ponderi  aqu^e  i  ium  ergi  globits  bracbio  li* 
hree  ajfixus  eft^  gravahmt  iUud  momeutQ  F^l^  Q  ^£ 


> 


/ 


%k  i^p  Si>Udm  fp$cifit9  jfr^ui  fluiS  tm 

mtJufH  deJtsndH  id  MUati  dijjefehtia  poHdtfum 
Jiib  todtfn  voluthiui  1  n«  6*  dijjiuniiM  ^taviiatiim' 
jlpccijie4rum  \  tiam  fdlidum  tale  ih  I^Uidd  atfiit« 
ter«  videtuf  tantQtidem  pondi^risii  quatitutn 
tft  pondu)  fluidi  fub  eodem  vdlumiM  e|(A 
pulfl^  defcendit  ergo  tion  totOi  fed  refidutf 
dtintaxat  jpondere  I  quod  efl  ipfa  difieitntU 
gr^Vitatam  rpedficarum* 

Cor0U.  t  £ild€iii  vis  idhife^A^^  t&  foti<io  kitm 

fltiidtitti  4>^cifiee  levl^s  fuftitiendd  ^  V<1  Attotiendo» 

Corotl.  tii  Soiidtitii  /^ecifice  leViiiS  lii^uldbgi^ 
tiOFe  peiiitns  ititietCnm  a&end^te  nititur  fi  ^qdall' 
dliferenti«  pondiirtini  Gxh  eod^tti  voltltnhiej  hitiiki^ 
ferentte  grivitdtttm  {pit^i&atiim* 

§«  dt)4«  GrMttstii  /pitifiia  foUdmm  pm^ 

dtri  d^ualiumfunt  Utiptrocc  Ut  poHdtra  iH  todtm 
fiuidd  amiffSi  Sunc  eisim  graVttate^  fpecifical 
folidorum  pdndere  «quilium  reeiproce  dC 
volaminii  (|;  6^*  Cor^  L)i  volumina  auteni 
fiuidt  expulu  ( qu^  titdetii  funt  cum  volumi« 
bus  (blidcfrum )  funt  dif e^e  ut  pondera  4  fiu 
iidis  jtmi/Ta}  ergo  gf  avitates  fpecifictf  folido* 
fum  idem  penaui  nabenttum  funt  feetproct 
ttt  pofidere  ifi  eodem  ftmdo  m\^i$ 

StifSh  11lebtiefti«  ptmftm  itCtt^U  ttpidfkiiii 
|fitiliti(iat  l^ificis  iorom  fete  folidertitiij  ^eoffi 

£i  i  ipoii* 


/ 

jfpVifi^tit  tniitiic  sqnaiiaiinr,  at  (pedfice  gnviora  Rint 

.codem  illo  fluido  ,  cui  immerguntQr.     Si  qu£  tamen 

.,    corpora  (pecifice  leviora  iint  Huido ,  e.  Cw  lignum^  i£to« 

ram  gravihtes  fpecificas  etiam  inveftigabis  cKplorahdo 

partcs  in  eodem  fluido  demerlas  j  in  quarum  ramm 

4ire6ia  ejfe  debent  gravitates  f^ecipcdt  foiidorttm  \    nam 

aequalium  {blidorum  partes  in  eodem  duido  demerfae 

'  lunt  ut  (^xpulfi  fiuidi  gravitates ,  quc  atquantur  gra« 

vitatibus  ablbkttis»  ac  proinde  etiam  Ipccificis  ipfb* 

rum  (blidorum;  ergo« 

§•29$.  Oravitates  fpecifics  fiuiJorum  junt 
dircBc  ut  pofkiira  ab  iodcm  foUdo  amifia.  Nam 
idem  {blidum  rucceHiye  diverlis  liquoribuf 
immerfiim  expellit  idem  fluidi  valumen; 
quarecum  gravitates  fpecific^  corporum  idem 
volumen  habentium  fint  dire^e  ut  pondera 
($•  ^3«  Cor.  //•),  pondera  autem  fluidorum 
€xpulfiirum  fint  proportionata  amiilis  pon« 
deribus  folidorum:  itidem  gravitates  ipecifi* 
cx  fluidorum  proportionatae  erunt  ponderi* 
biis  ab  eodem  (blido  amidis* 

Schol*  L  Rttrfiim  alii  in  detcrminandis  fluIdo« 
fum  gravitatibus  fpecificis  jconfugiunt  ad  varias  ejus* 
diem  (blidi  partes  (ticceirive  in  diverfis  fiuidis  demer* 
fas ,  JuHt  enim  gravitates  fpeeifica  fluidorum  reciproa 
nt partes  folldi  ihiis  demerfie.  Enimvero  cum  (olida 
ihiidis  impoiita  iiiergantur  eousque ,  dum  pondus  flui* 
cK  fiiiidi  expuKi  adfl?quet  pondus  totius  fblidi,  quod 
pro  fluido  luftentatur  (§•  eja.  Cor.  IL  ),  iden\  -effe 
debet  pondns  fluidi  cujuavis  expulii  ^  fi  idem  fblidum 
jmmerjg^atur.  Sunt  autem  fluidorum  idem  pondushaben- 
tiam  fpecificc  gravitatea  reciprocc  ut  voiumina  (  §•  6  j. 
Cor.l)',  voluminafluidorumfuntdired^ur  partcsde* 

mcr* 


..y 


Dc  motu  ftmdarwfh  4)7 

merftv  ^o  gr«vitates  fp^tficc  flaidorttm  fiint  rect-' 
proce  ut  partcs  iiiimer{k* 

V 

SchoL  IL  QoiiQ  viani  pkrumquc  ingrediama 
exptoraturi  gravitaces  (pecificat  corporum  five  (blid<^ 

.ram,  five  fiatdorum  ^  adhuc  paucis  docebo.  1«  Grom 
vitas  fpecffaa  mjtiivis  fluidifie  dtttrminatnr :  (btidom 
(peciflce  gravios  immergt  floido,  ca>as  gravitas  fytzU 
fiea  dcfiderator  ;  minuetor  pondut  fi)ltdi.  Eft  veroy 
pondus  «  foiido  &miflum  ut  pondos  fiutdi  idem  vo» 

^omen  llabentis  ($.  ^32*  )>  <]u^^<^  pondus  a  (biido  aroiC 

fnm  exhibebit  pondus  fiuidi  Uib  oodem  volumihe,  quod 

kabet  (bltdom  (§.  6^  Cor  IL),  Sit  cxcmptain  t  fruftumt 

trgentt,  quodtn  ^ereappendat  lo.  libras,  immer(uiil 

«quis  tppendie  9.,  libras  (  fi  enim  bilancts   brichiuti| 

ergcntoi  onuftnm  immerget  «qoCy   comperiet^prcvi» 

lerc  altcram  brachiom  extra  aqoas  fitum,  cdm  antew 

liac  cqoilibratft  eflent;  &  ad  cquilibritatem  denuQ 

inducendam  requiri  adiedionem  onius  librc  ad'  ar^ 

|;emam  ) ;  quare  pondot  aqnsr  fob  codem'  vUiftMnc 

eit  uniot  librc.       IL   Gravitatem  Jfiiiflcam  divtrfim. 

vum  fiuidorum  tKphrMs ,  fi  eandcm  maflam  e»  c.  ar« 

genti  prius  inaet^edecem  Itbrasappciiidentem^iycriit  tU 

Us  fiuidit  fiicceflive  immereet;  fic  enim  explorabtt 

(ut  (iipradixi)  graviuteai  ^cificam^ngolorum  fiiii* 

dorum  ^   qua  cognita  inhote(cere  deber  comparativt 

gravicas  (pecifica*       lll.  Qravit4tim  Jfttifieam  ^Jiver^ 

firum  filidorum  eemperies^  fi   qocvis  doo  fblida  di» 

verfum  volomen  faal^entiay  &  priot  in  aerecqoUibnu 

U  eidem  alicoi  floido  fimnl  immerget ;  experteritprtf« 

vaicfe  pondat  illiot  (blidi ,  cu|Ot  minos  fuertr  volaii 

vs  men ,  nam  cum  minot  liquidi  de  loco  (uo  depolerir, 
minot  pondot  amififle  videnir.  Hinc  ut  (bltdis  «rqui^ 
librion\  intra  aqnat  reftituatur ,  tlteri  volumioit  ma« 
ipris  (btido  adjicieadom  eft  pondot»  quod  defignae 
diSereiuiam,  qoc  (pecificas  tnter  graviutes  horuot 
cerporam  intercedit.       IV.  Grrjitas  fpeuficoi  filidi 

£e  I  *  etttn 


4^        &iih!h  e^m. 

imio  primuin  pondcrc  foli4i  in  ?crc ,  cxploratnr  |>on» 

l}a9  $)usdiBii|  Auidi^  imm^r^ ;  qMQ  f^f^o  eruitur  difFe^ 

^fientia  gravimilin  ffepi^m^m  6)Mi  6^  fluyiqmdeiii 
VbltifPioui. 

Sed  jam  fju^rer^  Iqbet  i  nihiine  t xptor^nd»  cor* 
pPFOfii  ^Qcer^  gr«vitati  ofHciar ,  6  XQrporum  CoUdQ^ 
rmii  pQndcra  in  ^ctp  prius  inveftigcntar,  po(le»  4n 
jlqidii?  ai:rcnifii  non  mtnus  ^uiduin  f& ,  qaaip  aqnn} 
l^rpinde  Hcut  aq^ai  aut  fli|id\iin   quodvil  aliud|  fiff 
9cr  49  vcro  folidi    pondcre  atiquid  dcccrpat.  eft  m* 
j^^fCf^,      Jjt.  Decerpic  omnino,  qnpd  mxinif^fto  cxpf»/ 
irim^nto  docpnnuF.      Si  globus  plumb^af ,  <Sc  ch«rt«* 
CCtM  in  licr^  Iil>cr9  ^uuipond^ranteii  lub  virrQm  reci« 
yicna^i^onitirugntqr ,   qc  rabinde  ope  mnchinc  pneu* 
in^iicqpi  ^^(h^nriatnr  ner ,  fqblatQ  #qailibrtO  pr^poilei 
|(lob(|S  phartgccos.       t]|c  vero  nefcip  ^  fi  alind  qoi4 

^uQ^  fubeire  poQit  ^  ^uam  :  qciod  in  air^  libcro  m^ 
l^f^m  ppnderji  fui  pm^m  nmiiiHe  yidwur ,  qasp  in 
faptto  fefc  ^xer^re  .ppreft.       Se4  Mmch   fi  fpppow 

VQlununenoq  miilcum  difrernnt,  ejns  ratio  bnberi 
9ion  (pl^t,  ^Q  etiam  ««  capir^,  quQsl  r«nis  «(i^odiiiii 
<it,  c^  enim  mnxra  «cjris  ad  maiTam  n^n^  fub  ^dcm 
yi^llimin^  «r  i ;  gpp* 

ScM.  T^bnbim ,  q«$  i?»Wbpai  diwftm  dlv^» 
ipriim  eprporum  grdvitatcm  fpecificam ,  adfpripfit  -W«« 

fgf^cfihroekius  ^  lol^TtiSiniws  ille  rcrnm  Qacurali^m  fi:ni« 
mtor  I  ^ui  indMitria  (li^  magnum  inter  Phyficos  «Qc 

m^n  fit>i  m^ritp  (im  conrciHt.     i^o  Cnr^pguint 

s 

JEfi  IfipQnifiim  ^  «         fi  ^W 

iEs  Siiccix  fwlvum  r  »  g,  78f 


» 

^ 


Antignofiiufn  crudmn.  ^ 

AmimonitiQi  Hnnggripom     <> 
Arg<^Pfa«n  puruin 
Aunun  puriijiiiiiuii} 
Pismathiiin  '      p 

Cbalybt  iiiA3(:ifP(:  «IfliUcns 
F^rum  r 

.>iAriciifiti    .  -^  .  - 

Mercorios  Geriii*nicii& 
Mcrcorins  BHt$onicos  • 

^Cinn^barit  nattva  "Xyx^^t 
«Cinnabtrlt  fii£fcitis  » 

Ploinbom  Briunnicam 
Plflinbiim  G^rmtfiiciim         •» 
Plombi  calx 

.^t^arhbi  ceniflt        «     .         v 
.{jjBth.fgyrigiin  tori       «  w 

Lytl  ^rgyrinm  ti^g^eini  ^ 

ScartMim  piinim  ^  •» 

£tc>noiim  poriflimiiai  AngUoim 
#^iim  ^ 

Aclifltes  ptlUde  ndim  « 

Admmss  r 

Alabaftrom  *  '     ^   ' 

Aliimen  plomolbm 

Amiantboa    '  .        ^     '         »  ' 

Attramentarios  lapit  riokceot 

Arfenlcom  robrom 

Arfenicom  flavam»  fire  turipigoKcntom 

BeryUot  ?  • 

Cameolos 

Ctleedomos  QrientaUt 

Cot  -      • 

E  r  4 


W 


r 


p 


r 


9>  149 
4i  ooo 

7*9 
640 

80) 

^« 

589 

S9S 
30P 


4 

fi 

t 

4, 


H 
11 

S 

II 
II 

8 

1 

7 
7 


1*5 

94» 
iS6 
epo 

04* 
«59 


».  «11 

3i  5»7 

l,  87» 

».  9IJ 
1.  «0* 
1,  «*| 
1.  }IS 

3>  05$ 
*,  >«» 

.1,  6^ 

/  Crc» 


^ 


tOktL  CfmPnL 


CryAdlm  r^tpmm  ▼slgirii 
Cnmim  D4shetnicm 
GraiMos  SoccicQS 
}lxiii»titcs  • 

Hy^^baAm  « 

/•dsicot 

Ltznli 

Ljdiof,  iamitraiar  Bf grom 

Magncs 

Bislachifcs 

VMtmor  IraKoifD  nigniiii 

Maroier  IcsKcqib  albuoi 

Msrnior  IrsHcum  aliod 

Kcpbrtticiis 

Onyx 

Opsliis 

OfAites 

Oftcocdlis 

Prcodocopazias         « 
Pyritc«  acrofas  ♦ 

Pyritct  fcrri  • 

Quarr^am  « 

SsrdaQhaccs  « 

"$ardoiiyx 
Ardc(i9  alba  • 

Ardeiia  nigrs  • 

Sclenirc»  • 

Silcx  yirlgaris         « 
Smaragdus  «    . 

Talcuip  Vcnctum  ^ 

Tophu^ ,  five  Tirai  .. 

Turcois 

TurmaUnnm  cryftsnaB  Qigra  (ataro  fismm« 

CQJoro  cx  IndU  OrUa(aU 


m,    650 


s,    500 

ft,   69S 

4,  5M 

«;  507 
^.  704 

V7»S 
«,  «94 
s,  5»« 
1,  ^5« 
*  s,  «SS 

5,  tt4« 

4,  ®«7 

4,  9«« 

«.  76| 

h  m 

!„  m 
1,4»« 

«,  95i 


vv 


Mtriim  albcim  Britannicum 

■^  itrum  viride         *  • 

Arena  valgari»  • 

"l.atcr«s  durl         •  * 

Bitumina ,  Sf  Saita, 

Birunien  purum ,  vcl  gfg^* 

Bitumcn  nig;rum 

Succinum  p^llucidnm 

Succiuum  aliud  ptngue 

Sulphor  nativum  rubruin 

Suiphur  vivvim         « 

Sulphur  vttlgarc  fufum 

/lumcn 

Borax 

!t^itrum  * 

Sal  Ammoniacum  parum 

Sil  g^fTm« 

Sal  mirabile  Glaubcri 

Hartarus  crudua        « 

n  arrari  cremor         «  ' 

Tartarus  vit^iolatua 

Viriiolum  Britannicuni 

Vitriolum  alt^ 


Uffuu 

Abiat  • 

Accr 

Alocy  fiveAfphalram 

Lignufh  Brifllam  riAimtn 

BUXQS  ,  • 

I^ignum  Campochia 
Codrua  • 

Coccoa  pQttmoD 
Ebenmn  • 

F«gut 

£o  ] 


44t 

0,   0Q< 


1,  744 
1,  065 

X,  087 

1,  871 

a,  ooQ 

1,    «OQ 
I,    714 

I,  7»0 
t,  451 

•a,  »41 
»,  »46 

h  849 
I,  900 

»,  «?8 
I,  880 

I,  $00 


0,  SSCI 

i,  *77 
i>  o|i 

1,  «It 
o»  9«! 
«»  «M 
I»  J40 

•1  711 

Quaia» 


^ 


44«  $$akllCi(mVBU 

Jpnipcrvis  -  ^  .  •  Qi  <l4 

Nephriricuni  .   *         -  ^         <*  I,  aio^ 

Prnnqi               t  V  *         ♦  Pi  ^*l 

StiH^fra^              ,.  -          g».  .      .  #,  48» 

Subcr                 .  ,p  -  O)  240 

TaxHI          •       -  -^  *  P,  76Q 

tJimtti         '       w  '       9  9  p^  6p9 

l^ignam  rirtegituai  Vitgipic  r  h  V% 

l^ignwin  rit*      .  ♦  «  '  '1  1*7 

Hadix  Chin<  .              1»  ^  i|  071 

Cortcj^  PcraViinni  '        »  -  o,  ySf 

Galla            %  -        •  .  I,  «34. 

Cimphort    "      ,  «  ♦  p,  996 

Ccridm     *     ^  *        •»  -  or,  955 

Qummi  Ari^icttni  «#  -  »,17$ 

Myrrhi  r    .       ,**  •  .  t^  ?5«> 

Ppiqm          '      »  ^  -          *  I>  J<^J 

^ix              ^  *  ^  -  I,  150 

Befina  Guaiact  '       «^  *  f,  ^^4 

Befipi  Scimmgmi  •  *           ••  t,  100 

£s(pQh«btqr  bio  ginyiw^  Q>«Gi^  Iq  ^lUonk 
bui  decimilibai  ^  qnai  1  nnmerti  inregrii  iiparac  in« 
lerpoGta  lineoht  $tiiDif«M^  it«n>  (pecifici  aquc  gr«- 
f i(ll  ?t  I»  000  ;  binc  ^  CoUtfom  iulpbur  vivpm  ^ 

Qoi  rp^iictm  corponiip  gavitattm  p^perirt  ipll 
Vol^t ,  ^4v9rtit  rpUm  I  tf mpcrato  aere  cxperim^m»  Oi» 
pi|i>ija  effe  ?  non  niniiifrigido,  non  nimii  cai^tf  ^^ 
)7e  fbrtp  Uq^i^rum  ^(^  frigore  eonftrifionimt  &a 
9llorc  fUlattktorum  ^oiltii  ^Ut  raritit  ja  oniflii.  fir^ 
^SioA  ho^io  rppertjp  {;r9vita|$t  ^ecific#  iioii  confin* 

m»r  illf$  I  M«if(b«f>brskio  ootitiif 


jhUdorHn  ifffiuiais,  n4n\  poiita  fsadfm  6gur4 
globi  ferrei,  &  jigncl  m^rgirpr  in  ^odem 
liii()uof|uido  ferreuS|  innaMt  ligni;^i|S}  ergo^ 
11«  (cl<fm  globus  ferr^ps  diverfi^i  flnidis  corn* 
ipiflus  qelerias  defc^ndir.in  uno^  quam  alio^ 
0,0»  ccl^rius.in  fpmt^^  vini ,  quam  in  a^ua^ 
Qiii nam  vero  iilud  6eri  point,  fiquidem  R^ 
gura  (it  c^u(Ta  merfionis  I  Hm^  manente  ^ 
dem  (aaiTa  manere   d^b^t  id<m  effci^u^i 

«rgOf 

ff  $37f  Cliii//i  nnr/iomi  /ilidmm  infiuUU 
$PfgrmnUf  r$fpf^iv§^  (joam  bfC  loci  vocabo 
wceffum  grayitaw  fpecificap  folidi  fupra  (pe* 
Cf ficam  fluidi  9  Of  c,  globi  ferre;  fiipri  grayir 
fntem  a9U«  ejusd^m  TolQmintit  fr,  Merg{ 
f  d  defcendere  ih  finidis  {  fed  cauH^  defcen* 
fas  in  flujciis  ed  diffcrenti^  gr^vitituro  (bwi^ 
fic4rum  (Sf  3)3f)9lif  e»  grjivitw  refpciS^iva} 
ergo,  C9mm,  l,  PofitemaiorifpeciSc^gr*-? 
Titite  (blidi  bibecur  merfio ,  ««^ue  non  po« 
(iffi  non  h9betiir|  ergo  majorflUgP4vitas(b« 
]idi»  qu^m  fit  (fuidi»  eft  aufla  merGonist 
^nfirnh  H  PoGta  eadem  graviwe  fpccific» 

fc«betur  celerior  cJe(cen(Us  jn  un<nrtguoflui* 

do,  quem  tn  alio ;  ec  {^ropterea  celerioris  de« 

lceniTMa  ciqini^  gravitis  re(pei%iY« }  qHidni 
igitur  Sc  merGonis  ? 

lnaMr(i(ni  ainittit  gravitfltem  fwqi  ( |t  %}•• )  j   M« 

cflf 


444         ^^^  n.  opminir. 

eflfe  grtvittt  rtfyeettv^,  ^^.  Dt  A.  SoliJQRi  (pecifice 
lcviiis  (luido ,  auc  e)iudein  gravitAtis  fpecificae  smittit 
gravtraxeQi  C,  A.  fpecifice  gravius  fluido  Subd,  «mit- 
tit  gr0vitiiteni  (Uam  non  omnem  C,  A.  omnem  W«  A. 
&  C.  partem  duntasat  ponderis  amittere  videtur  (b* 
lidum  mer(um  ,  eamque  non  majorem  ^  quam  qux 
ex^qiiet  volumen  fluidi  expuUi ;  reliqtio  pondere ,  ii* 
ve  differentia  ,  &  excefTQ  gravitatis  dc(eendit  fblidam» 

II.  Si  gravitas  dieenda  flt  caaiTa  delcenCiis  ,  & 
fherfionis  non  poterit  ideoi  (blidam  in  eodein  flaido 
)aiti  dehtfcere ,  jam  enatare  ,  jam  denique  rar(iim 
mergi.  lltud  vero  fieri  vide^ius  in  pifcibps ,  cadavere 
hQmano  ,  globo  vicreo ,  aut  quovis  alio ,  (e4  cavo  ; 
^go» '  1^2»  D,  M,  non  poflbt  iAud  fieri  ntaiienre  eo* 
dem  volumine  tum  liquidi ,  tum  (biidi  .C.  M«  alteni* 
tro  miitato  N*  M..  atqui  fit  iftud  aiteratro  mtitato  C,' 
m.  utroque  permancnte  N.  m,  fic  C.  Haic ,  huiu^f 
qHQ  (imilibus  ajiiis  objcAtonibus  ut  rite  (etisiiat,  -  nofTc 
oportet  omnia ,  qu2  (bperius  dixi.' 

III,  Etism  manente  eodem  volumine  cum  (blidi^ 
tom  fluidi  npn  merguntur  corpore  graviora  ;  ergo, 
Pr.  A.  Scobs  ferrea ,  ant  qinevis  minotiffima  metaUo- 
rom  frofta  flQidis  tnnatant,  tametfi  graviora  fint  parl 
volumine  flQidi,  fiihilque  immQtetnr  volumen  five  flui- 
diy  (eQ  (blidi^  ergo«^    l|t.  D<  A%  nmi  mergQmor 

Sl^raviora ,  fi  eorum  gravitas  non  fit  expedita  C.  A, 
ecQs  Nf  A*  &  C,  majorem  gravitatem  ,  (eu  ni(hQi 
defcendendi  cobibere  poteft  major  fiuidorQm  vifcofitas, 
etuqu^visdia  id  genus  nflTeQiOi  cai  (bperandie  non  fii& 
ficit  ilia  gravitas  refi)e&iv1i ,  qast  reperitur  in  minimis 
hifce  meteilorum  frQftoIis.  Dke$  :  Gravitas  re*  ^ 
(peQiva  (cobis  ferre^  pror(bs  eadem  eft  eum  illa  tottm 
inafT^p  fcrrre«  nondum  in  minatas  partes  iiviEt',  fed 
^revitas  re(pe£tiva  totiua  vmSm  ferrtae  vincit  floido«  ^  ; 
rtim  wdfiofitatem  ,  eot  quamvit  aliam  aflfedionem  ;' 
igttnr  <k  feobi  ferm  Tinoerc  debtret,    Nen  sBtaa 

vin- 


D$  ffioiu  fiuidortm,  449 

Tlntttt;  ergo.  :^.  N.  M*  Licet  rcobem  ^errestn 
conttituant  «xdem  tnoleculs^  quxe  prius  maiiain  to^ 
tatn ,  cre(cic  tanien  moles  in  fcobe  fcrrea  cx  fa^Va  di« 
Viiionc  molecularuro  ^  ortisquft  adeo  pluriitlis  incer* 
ftitiolb  inter  iingula  molecularum  paria  repertundis* 
Majori  hiiic  tnoli  proportionata  eft  major  refif^ctiria 
Huidi  ex  partium  Vi(cofitate  ,  ac  tcnficitate  provenlens* 
Alia  reiponiio  facile  crnetur  ex  infra  citcendis. 

IV.   Gk>bus^  qncm  t$rmefitarium  dktrz  foktit^ 

aquis  tnarinis  inje^lus  dehifcit  ad  certam  aliquam  pro* 

funditatem  ^  e.  c«  ad  medium  ufque  maris  i  deincep» 

immotus  hsret ,    ad  fundum   non  delabitur.     Atqui 

globus  iftc  gravior  eit  pari  volumine  aqua&i;  ergo  iton 

omnia  corpora  ipecifice  graviora  merguntur.     i^*  D. 

M.   dehiicit  ad  certam  uique 'profunditatem  ,  ii  funi 

iiligetur  C.  Mt  hoic  ii  non  iliigetur  M.  M«  acqui  glo« 

bus  ifte  ieoriim  fiimptos  gravior  <(k  pari  voluminc 

aqiis  C  m.  iiimptus  cum  fnn^  ex  auo  petidet ,  live 

cui  iiligatur  N.  m.  ^  C.  globus  ieoriim  (omptus  ^e% 

cifice  gravior  tA  quibusvis  aquis  ;   ied  &  ad  fanduni' 

ofque  dcfcendit.    Si  tAmen  fimi  illigatos  aim   fiine 

defluo  ilelcendit ,  non  globi  iblom  ratio  habenda  eil  ^ 

ied  vcro  ettam  fnnis  bene  longi ,  quorum  otriufqoe 

volominibos  fi  refpondeant  paria  aqoc  voioroina,  roa« 

jorem  eile  oportet  gravitatem  aquanmi ,  qoam  gtobi, 

4c  fonis  conjunffim  fompti.     Scribont  alii  ^  in  caoiie 

.eife  msjorcm  aqoarom  marinarom  gravitatem  propei 

fbndom^  quam  (nperiiciem*     Sic  ajimt  }  prope.  fbn* 

dum  babetur  major  aquarum  ,  aot  verius  fluidi  alte- 

rios »  ne(cio  cojus»  eompreifio ,  propter  liHtioreiii  alti« 

nadtnem  coiomnarom  verticaliter  prementiumi     sdo  s 

prope  iondom  aqiie  mAjore  copia  fidis  onerator  (  ho» 

die  enim  ialiedinem  maris  pieriqoe  omnet  repetaiir 

e  ropibos  ^  vel  fodintt  ialiom  in  fondo  meri»  dditdS 

€c«cU>ot  I   qoarom  perm  eqoe  merina  corrodit ,  ie«^ 


44^       m»ttc$f»m 

^Ue  liKlea  otmat  )  ;  qdodrM  gniibM  iA»  ti.  ei|ilM 
grariot  «fBcita^  dlOo  globo/  hinc  lion  iubfidit^ 

Vi  Sl  grivitu  fit  Cibl&  OierGcnij ,  itOh  poteranf 
mm  Diagnit  pondcribtit  onDllc  aqiii)  tnnatartfi  Jm 
Aatant  auitin  }  «tgo.  Pr.  Mi  Graritii  ligni ,  f^rrv 
tncnloruni ,  &  tel  maxjme  |M)iKleruin  navi  adjc£toi 
f  om  major  efte  vidatnr ,  ^nam  fit  llla  aqiUrem  ^  «k  & 
fi  in  tiavim  tUinjiciai  vaQi  auro  i  Mercurio)  argdnto^ 
«litique  metallia  fcfena  ;  ttvp  il  graVitai  fit  &)d£Gi 
dMrnonb,  dcbifcet  naviii  anfiniti  minot  tft  gi  avk 
taa  poiMktnin  ^  qiiz  nivi  'Vdiontttr  fingalatim  fimi' 
Jttotam,  qnam  ponderl  tiatia  idjcfiarbm;  atqtti  fiit* 
fiUlatiin  fitinpta  mergDDtar  ,  fimiliter  crgo  idjtiAi 
pondnl  nivia  inergi  debent  i  qtiod  falUrt  ^^  N<  M. 
•d  Pfi  Di  A>  gravitai  paftdcrutn  iingtllidttl  fumpcO' 
rmn  inajor  tSk  C.  A.  (iimprontm  cnm  volnniine  luvil 
K'  A.  &  Ct  Si  pehei  ttavim  conlidetinttir  foU  vOlD' 
ibina  iigAti  ferrametito^tun  ,  &  ponderum,  qtiibui  tn 
'  tleritiir  navia/  aftf  fateor,  illii  rerpondeuirolnmen^ 
qdtt  (p«dfice-l«viuE.  Scd  antcm  limnl 'attendeflda  efi 
M^tai  navii,  rolamcnqtie  iftiDl  Cavifatii  addcnduffi 
ttbqtW  Toltniiini  jiavit }  prtM  enim ,  quatt  tota  tiavia 
ln«|;eretar ,  de  loco  fno  ejctnrbandam  eflet  volufncfl 
«jos  relpondcn*  tton  nodo  di&ia  pondiribas ,  fed 
cdam  eatkiti.  TaJe  «atc«  voitunen  eqac  graviBt  e(t 
fUvi  fiuttptciam  oneribaa  <djeAii  j  navii  itaque  mer< 
|i  aui  debet'  Qaomodo  eon&ltiatio&i  fMislaCieAi 
«ta  t  «bwido  ^t. 

MQoU  hofiaMMiJitef  idipotiu  cqaii 
i  vero  ttot  lUa  ptfiiia!  tA  fnri  tol»     v 
go<     $<  C^  M<  K<  m.  tirea  aewi' 

tindiqaa  ef^ttiKttir  eavltatj  Cbjtii 
i^te  fltffi  iti  (tronath  «ft  ,  ut  eit> 
MriaMkto  eiiMt){tf  otiare.    Pof  ro  vollM 

voluniiM  avlmii  effofmrita  fitntil 
iadf 


Affifiltt  tt€|li%tietlditBf  {Mf  T^fttntetl   «^tiif  ^ffc  ^^ttH. 
liter  grave^   qtulre  aclii  merginoti  debtt. 

Vli^  Fa!>«  Ai^ebtctr «  facci  ti^rbaratti  ^  (al  ^  &  &e* 
dhAnim  gratiora  fiidt  pati  voitittiifie  aquar/  nee  ramciiv 
tnergtitittit ,  led  fingitlit  aquii  niolecdlia  innarantj^ 
gravitas  ergo  tfM  eft  catifla  itief (ioniii  ftefpondettf 
aliqui :  it^terc^dare  hoc  eaftt  pirticulareifi  caniiani ,  i 
qua-prff fcindettdom  eflef titaiir.  Ito&ati  s  qo^tiam  iif^ 
caufla  ilift  partlcoiif b  effeietia «  ot  dlablotit  fabammi 
(accharl  &c>  ttlolecol*  poroa  aqotfc  fobeant  ^  &  iit  iii 
Atfl!ineant6r )  repontmt  t  notidam  convenfre  ititef 
^hyitCdtt ,  at  adtaae  fiib  todiee  litem  efle<  Alii  eao(^ 
iam  eoniiefitnt  iti  exil^em  ^  ae  tenoitatem  moleculi' 
ttnti  diviAriim  ^  quartlm  gfavitai  mitiime  (lifBcietis  (ijC 

ed  vitteendam  partium  Htiidonim  tohdloitem  ^  aiit  te^' 
tiacitatem^  Alii  deniqoe  iit  mofttm  inteftittiim  p^^t^ 
thim  minimaromi  ^  quo  fobiltde  immitioto  ,  ittt  pfd* 
pe  evatiefctnte^  ecklm  miitimc  mohcuis  fillum  ^  (ie- 
ehari  dic^  ad  fondam  dchiicatit  ^  uti  oempe  evenlro 
folet  aquli  eofeti  quOpiaiti  tittQlii 

Vllt  Avei  fpeeiiiee  gi^l^Ofei  littit  ittti  tfdtitlt 
timen  i  fttdeiititttar  ab  aere  ^  tteque  urgente  graviti« 
te  refpeCitva  deiSfeiidmtf  i  ergtt^  l^.  C.  t.  p*  A«  D.  u 
volant  temett^  (At^ter  motom  ^  qoem  (ibi  Imprimotit^ 
(itiiitietifarmii  ok  cii^  fortiter  verberiti  ierii  C^  A* 
volarent  <  d  Itce  ibetfent  f4«  A«  &  C  iVia  voUre  cti« 
fifieni  primo  libi  mdtom  qoemitiim  ittiprimif  ^  toiii 
etii^tti  aiii  jbrtiflimtf  ier eiti  verberat^  Sie  verberi^ 
tas  ier  evidlt  tiiiqaeiill^  |taii6htm  femm  ^  quo  ivia  d* 
fltentitort    Etiimqttc  ad  volatom  ii^ttm  eoiifert  ili« 

fOm ,  dt  eaodof  etfiatiivO  ^  «e  ditifitio  ^  lie  eniill  mi« 
jos  votumeit  aeris)  re^oitdet  levii&miti  onmitio  pttu 
Aii.    Eodem  fero  medianilitio  «ilplieiiidom  ift^  qoo4 

homiiiei  (pkifieo  gfliviorci  •qotf  intiitimi 

*.'      .  •  •  *,  '  ^ 


44i  SiShth  GafmPSh 

IX.  Corpor«  rpect6<:e  IcYiofft  ftpe  ktifil^tllllr-liA 
ftili<ium;  efgo  grAvitas  tcCfn^&vfA  non^.cil  caii^.merk 
fionisv       Pn  A.    Spongia,  frujElus  hortenfes^  panis^ 
lignofttnl  fegmenta^   rrabti    iifimo  &c».ieViora  fiint 
pari  voiaitiine  «qniKj  &p«  tanieti  tti^rgontur;.  ttgOk 
Cwfirm.  Experientia  certuin  habemui  non  mtt^i  la» 
genam  vacuim  t  vitro  conflAttm^  qus  eadem  fi  iluido 
iqueo  repleattur  i   eontinuo  fondum  petit*       Eft  vrro 
bgetla  aquis  repletaadhuc  l^^x  pari  ¥oJi?niine  aqu^e  i 
€rgo<       Pr.  91»  Volumen  «ijiMs  re(pondeni  volomini 
iblius  vitri  eft  gravius  vitro  (  anc  certe  t  ti  leviut  tft^ 
debet  iagena  vacua  adimum  dthi(cert).       Volttmcit 
aqusB  rt(pondens  volumini.  akerius  aqud?  lagent  con» 
firi^s  cqot  grave  eil  \   ergo  lagena  aquis  repleta  l^ 
Vior  eft  parivoiuhiine  aqua?»  >  Mtrg^tur  tamcn^'  proitt* 
de.  qt.  N.  A*  ad  Pr»  D»  A».Scofai  lignea,  frudqs  horttn» 
fts,  ipongja  &Ct  roerguntur)  poftqoam  aqua  per  poroi 
&beunct  in  iocbm  acris  eyaftrunt  graviora  C.  At  qoain» 
dio  intra  eorporum  iflorom  poros  adhuc  iatet  aer  K* 
A.  &  C.       Ad  C0ufirm.  C.  M.  N.  m.  adPr.  K.  1« 
{>•  A*  Voltimtn  (biius  vitri  gmvi^s  e(l  pari  voiumtnt 
aqu^.  .      Qood  tamen  iiagena  Vactia  non  mergatur  |  • 
ttibotndum  tft  nOn  modo  vitrO  j  fed  &  aeri  iagentt 
cavitatem  txpitnti  1  quorum  duorom  fimulfnmpt^rutH 
trolumen  itvius  tft  pari  voiumintaqus.       Sic  quidcm 
faciie  txptditur  obje&io  prflriens*  -    At  ii  Vafi  vifrtg 
lobftitnatQr  vaa  Ugmuim^  t«(iirgert  viMuftr^  &on  mo* 
dica  diffituitas« 

X.  Kihil  Immotita  ^ivitatt^  diii^iliat  «tmtalA 
^gura  jam  mtrgicor ,  |am  iioij^  innatac  corpos  Ibli* 
dumi }  trgo  non  gravicas  |  (td  figora  tft  caufla  mtr» 
iionis.  P»  A»^  Eadtm  mafta  plombi  Q>barrain  c^tis 
^icns  mtrgicuri  tademqut  in  iamtliam  cn(a)  &  di« 
dfi£la  (bpernauc,  ergo*  l^»  D«  A*  Nihil  immocata 
ftwrkatc  aifiluia  corpus  iam  mtrgitori  jam  (uptrtia»* 
M&Af^Hrii^^Ni^filCi       Ad  l^n D. A.  6i<*. 

fatt«  ' 


iiultiil  in  laini^ikim  didtidtis  fap^maUt  p^dptir  itnmU 
fmtam  gtavittHetm  ^ecificam  G.  hxauffa  nova  figur^ 
Nk  A%  &  C.  Si  quid  figutc  tf  ibtiendtifn  (it ,  dicatur  ^ 
J^er^mi^iicet)  occafito  noviter  dcgUiiir^  gravitatis  fpeci* 
fics.  .  Sed  in  hoc  ipfb  diiucide  expUcando  6ft  difiir 
tuitas.  Fars  Una  (ic  putant :  intitr  •ejitsmodi  Idminav» 
tktcunqui^  poUtaiU ,  &  fluidum  fe  infitluat  aer  ;  undo 
lotuth  aggregatuiti  ex  aerd )  &  lamina  (pe6landuiti  eil 
ceu  corpus  unum  ^  t^uod  au^a  (ic  mole  levaiit  (pecifico 
levitii  Volattiine  aqux  «xpeliendo/  Pars  aitera  (ic 
«xiftimant :  Manfa  globi  plumbei  iit\  lamciiam  didu£li 
foiitarie  eotiiideranda  xion  eft^  (ed  cum  ekvitatei  qufl» 
tirca  ipfam  undique  eflbritiatm:  prius  ,  quam  tota  im» 
Ikiergatur  aquiv.  Dicunt :  obfcrvatiohiboii  fspe  adhi- 
bitis  exploratum  efle  5  <}uod  cik^^a  laminam  fluido  len* 
te  impoiitam  aqti^  artoUantui^  undique  in  fpec'em  coU 
iiculorum  eam  dngenciun)  (  forte  ob  cohsiionem  )  ^ 
Heque  tamen  ad  laminam  deidaaint  (  Ut  fieri  videmus 
penes  vitr^a  Huido  abunddtiter  txpleta )  ;  hinc ,  iftis 
.jquidem  au£lotibUs )  promitieiitia  iila  aqu^  id^fn  pr«« 
ftat ,  tanquam  fi  lamina  cingeretUr  lateribus  (blidit 
Verticaliter  ere£lis  ad  inodicam  altttudinem  aflurgen* 
gentibus  in  tUodum  navicul^^  Sic  vero  facile  ex  t« 
lias  di£lis  conjidtur  ratio  \  tob  quam  lamina  plumbe^ 
«iquis  intiarare  debeat.  Dices  t  illud  eft  caufla  merfio* 
jnis,  quo  pofito  merguntur,  &  notl  pofito  non  iner« 
gumur  torpora ;  (ed  pofitd  tiguta  t.  c.  fph^rica  mer- 
guntur  corporay  noii  pofita  non  merguntur  ;  ergo^  . 
I^.  illud  eft  caufld  ^  quo  pofitd  ceu  ratione  formaii^ 
&  Aitt&ii  ^  ^e  imitiediata  ^^  jtnerguntur  corpora  C.  M;  • 
jceu  conditione  prsvid  lid  obtinendam  majorem  gravi- 
tatem  (pecificam  ,  dut  ad  facilius  fuperandam  refifteii» 
tiam  medii  N.  M^    SiC  D«  ni<  &  N.  C« 

XI.  Figurft  cft  caufla  <«eleri6ris  Jefcenfui  in  tktt* 
1^0 1  ergo  &  merfionis  i  niiia  cadem ,  puto,  utriu(quft 
pSiSk  couftUtti  dcb€t.    iPn  A»  mafli  fem  in  fphdsrain 

FS  «  69ti€ti 


COifia  celeriiit  deicendit,  gnani  eadeai  i^tfli  ihtfk* 
hxxtti  fonnata ;  ergo.  9«  N.  A»  ad  Pr.  D«  A.  mftllk 
ferri  in  f^h^ram  coa£laceieriasde)(cendic,  quia  mfljoi? 
«ft  grayttaa  f^mfiea  fyYtsttx^  qoam  cobi  C.  A.  proptec 
iignram  fphnicam  SubdifL  per  aecidens,  quatenna 
fnmau  cabi  fignra  in  {phcram  mutatur  gravitas  ipeci- 
fica  C«  A«  direde,  acper^-fe  N.  A«  &  C«  qao  minos 
voinmen  ejasdem  alicajus  mafls ,  hoc  major  feft  gravi'« 
tas  (pecifica  ;  e(l  vero  minus  volumen  d^hxxx  ,  quam 
cnbi :  proinde  major  gravitas  (pjscifica  ejusdem  maflk 
'^hjericie,  quam  cubicft;  bincitidem  celerior  defcen» 
iiis»  tdo  :  Cobo  ferreo  refpondet  major  fbpcrficiet 
fiuidi  de  loco  fuo  dimovendii  acque  adeo  major  rcfi<« 
fientia,  majorque  firifiipf  ft  Q^  denoo  repcti  poteft 
tardtor  dcfcenfiis. 


^ 


De  fluidls  e  vafe  profluentibus^ 

%.  2  3  8«  Si  pnffid  fttddi  aJi^ua  ex  parta 
%^Uitur  f  vel  minuitur ,  movnur  fiuidum  in  €am 
fartcm^  ubi  ^tjfio  fMata^  vtl  minuta  fuit,  Sem« 
per  enim  dtficienti  virium  aquiUbritat^  habetur 
jnotvLsfieundum  dctertpinatiomm  vis  pr^evalentis  i 
crgo  u  preflioni  preffio  aequalis  non  refpon-» 
det  I  aut  omnino  fublata  fuit »  feretor  hqui« 
fium  in  eam  partem  ^  ubi  preffia  fublata  mt^ 
irel  minuta, 

Schol  Hincefl,  quod  foramine  in  fundo  ^  aut 
iatere  vafis  fzQo  liquida  erunipunt;  hinc  iteruiri,  qnod       ^ 
•qua  afcendit ,  fi  e  tubo  fiiperficiei  aqus  jmpofito  ae« 
rem  exfugis ,  atque  ita  fiibieftan)  n^uc  portionem  ao» 

iris  prei&one  liberiib 


'^D^  fHotu  fluiJorumi  4^t 

§.  2?9.  Ctkrita$  fluidi  ex  eoJcm  vafe  frc^ 
Jlumtit  eadem  efl  in  iitdcm  a  fuperficie  liquidi  di^  ' 
fiantiis  ^  diverfa  indiverjtti^  nam  celeritas  rc- 
fpondere  debet  preflloni  ,  ceu  effeAus  yj 
&  c^wiXdi  Cux ;  fed  prefliones  in  fundum 
ejusdcni  vafis  funt  irf  ratipne  altituc|inuin 
l§.  aii.  OroU.)  ;  Cmiliter  ergq  celerit«ctf 
fluidorum  cxeodem  vafe^profluentium  etrunc 
in  ratione  altitudinum.  Altitudines  fluido- 
rum  funt  difhntiae  a  iuperficie ;  ergo. 

Cor4>U,  L  Si  vas,  c  quo  iiuidtim  mimpit ,  fiierit 
<;onAancer  pl^num  ,  fempec  eadcm  crit  altituda  Aau 
di ;  quocirca  fempcr  eadem  cclcrjtare  fluiduia  «rum* 

Cort>n,  IL  Etiam  cclcritas  fluldi  profliientis  o 
duobus  vafis  candem  lidim  habenribus  eadem  cft  in 
«qualibus  a  fupcrficic  liquidi  diftanriis ,  divcrd  in  di- 
vcrfis  ;  pofita  cnim  atqualitate  bafium  prciffiones ,  ac 
proindc  celciitatcs  funt  in  rationc  direaa  alritudinum 

$.  fll^a  C^itaiet  flmderum  per  e^uglitk 
foramina ,  aut  lumina  erumpetttiUm  funt  utflmdo^ 
rum  quantitatet  evdem  tempare  effufa.  Has  enim 
quantitates  fpeAari  poffunt  inftar  cylindro^ 
rum  eandem  ba^m  baUnUum^  quorum  fo[idita« 
tcs  funt  ut  altitudines  (  fer  Stereom. ).  Porra 
motus  intra  foramina  hid^cri  pofefi  pro  »« 
quabili ;  cumque  in  motu  aequabili  ^lent** 
tcs  fint  ut  (patia  eodem  tempore  confe^a^ 
trunt  nofiro  cafu  ut  cylindrorum  alpuidi* 
oes  I  ti«  €• .  ut  quantitates  flaidorum  eodcia 

«cBjpor*  crittopcntest   ,     .  ,;^ 


«,  > 

V 


I*  > 


4J9  Si&id  11  CaputVIlL 

SchoL  Motus  intra  forjiinina  confiderart  pottft 
•t  squabilis ,  quia  motu$  intra  foramina  habetur  pro 
inftantancb  j  qnacunque  atitcm  lcge  tccclcrctur  ,  aut 
rctardctur  motus,  (cmpcr  inftantancu»  pro  ^quabiU 
habvri  poteft  (  §«  173  )  • 

%%  24^  CcUritAUi  fiuidorum  per  d^uatid 
firamins  effluintium  funt  utradicti  quadrata  aU 
titudimm  ^  quai  fluida  obtinent  fufra  foramina  ; 
fire  :  C  r=  r  A\t;cC\  c  ^  r  Ax  r  ^^ 
Nam  celeritate^s  fiuidorum  pendetit  a  preffio» 
tie;  pofita  autem  ;drqualitate  bafitim  preflio-» 
tie^  iunt  ut  altitudine^  (  %.  221«  CoroU.  )  ; 
quare  fi  preflionem  dicas  P  ,  &  altitudinem 
A^  eritP;=:  A^  Preflionts  efFe<5tus  e(l  quan^ 
titas  motus^fivejPi:  Af  C}  fiq;  maflam  fluidi 
profluentis  voces  ^  ,  habetur  P  -:  ^C; 
proinde  etiam  if  i=:  ^  C  (  §♦  i.  4Ar»  /F. )  *  ^  i 
yero  :=:  C  (  §.fraced.)  ;  ergo^C  s=:  CCj^  i 
ideoque  i<  =3  CC^  Utrinque  radicem  extra* 
hendo  obtinebis  Ca  rA^  five  C:  ^ «  rAt 

^  CoroU.L  Qtkvim^  fluidforum  persqoalia  fb* 
ramina  crumpentium  fimt  ut  fluidorom  quantitatca 
eodem  tempore  cfFufe  (  §.prae. ) ;  crgo  ficut  celcri. 
tates  funt  in  ratione  fubdupiicata  altitudinum  ($. 
pr^fenU ) ,  fic  quantitatcs  fluidorum  pcr  squalia  Jo* 
niina  enimpcntium  J  b.  e.  P  a  ^-4  ;  &  jP :  a  =5  /    . 

CoroU.  Ih  Etiam  in  motu  uniformlt^  accelerato 
eft  C  :  c  -j  t^S :  f^  s  (^.  160.  CoroU.  VIII. )  ,  five 
celeritatcs  finalea  font  in  rat.  fubdupl.  altitudinum, 

tx  ^uibuf  inobilc  meta  tifiiformitei:  accdcrato  de(cea# 
■  dit; 


^  )  Si  motu  JtuidorufHk  4$% 

dit;  ergo  celeritas  fluidi  ex  V4(e  erumpenHs  tanta  efty 
quantam  flqidum  acquirerec,  (I  lapfn  perpendicuiari 
defcenderet  ex  eadem  alticudine.  Qjiare  fluidum  mo* 
tu  retardaco  aflfurgcre  poterit  ad  eandem  altitudinemy 
inotu  autem  xquabili  ad  duplam  (§.160.  CoreUAy.J^ 
'  ^eqtie  dicof  t  iflud  locum  habere  pofTe  y  fi  va(a  perfo- 
rentur  iii  fundo  ;  non  autem  fi  in  lacere  :  aut  (i  va(« 
fuerint  inclinaca.  i^.  enim :  etiam  obtinere  debere 
penes  vaia  ti  }atcre  aperta ,  cum  fluidapremant  atqua- 
liter  in  omnem  parcem  ;  ctiamque  penes  vala  incUnt- 
ta  (jr«)o},  ^  2Q6f). 

§•  242.  Si  va/i  fuertnt  conjlantcr  pkn§ , 
^^ue  altituMnes  fiuidi  confianter  aquales  ^  tadem 
ceUritate  erumpet  fiuidum  per  foramina  auauis 
utcunijue ^  diverfa.  Cogit£tuF  enim  foramea 
majus  dividi  in  plura  loramina»  auxfingula 
.squalia  finc  foramini  minort  vaus  altenus. 
Pofita  eadem  altitudine^  &  fofaminum  jc. 
qualitate  haberi  debec  eadem  celeritas  iVt 
finguUs^  partibus  majoris  foramims  »  qus^  eft  in 
minori)  cum  ubique  prorfiis  eadem  habeatur 
predio  (§«221.  j;  proinde  etiam  in  totoma^ 
jori  foramim  eadem  erit  celeritas  ^  quas  in  mU 
nori. 

%.  243«  In  eadem  bypothefi  quantitates  fiul* 
iorum  eodem  tempori  erumpentium  funt  direSa  ut 
foramina.    Si  enira  fluida  in  vafis  conllanter 

{>lenis  obtinenc  altitudines  conftanter  a^qua* 
es,  fieri  fane  debet»  ut  eodem  temporepe( 
aequalia  foramina  xqualis  fiuidorum  quantitas 
efiUndatur;  quare  e  foramine  dupIoefFun*    r^ 
detur  qaaotitas  dupla  ,  c  triplo  tripla  &Cr  C 

Ffg  •         Sic       . 


# 


i  ^ 


t 

^tte  Ukleiii  otierat  )  ;  qiiodrei  gemino  lAo  «t  €ipiM 
^rmot  cfficitalr  diAo  globo  /  btnc  boti  rubfidit^ 

V«  Si  grivitu  fit  eaoflk  Oieirfionis  4  itoh  pOteront 
i|iV«t  nuignis  pondedboi  onoflft  eqoit  intiir^rtfa     In» 
tiitant  auttiii )  crgo*      Pr.  Ma  Gtevitit  ligtit ,  ferra* 
merttorttm  ^  &  Irel  tliixini^  }M)nderuin   nairi  adje^o* 
f  um  major  elTe  videtur «  quim  fit  llla  aqoirum  ^  o^  & 
&  Itl  havtm  donjicias  vafib  iOro  1  Mctrcurio  ^  arg[Otiro^ 
Olitaqae  metiliis  feferta  ;   ergO  (!  graVitas  fit  6aafli 
ttiernonisi  debiicet  tlavis*     Cenfirtn*    mioor  tft  giaVi» 
las  ponderotn  j  qost  Oavi  'Vehotitttr  (iiigolatim   (um« 
ptof om ,  qoam  portderi  tiav^  idjefiorom  i  atqtti  flil* 
gtiiatim  fiitnpta  mergontar  ^   fimiiiter  crgo   ad}tfdi 
poodtiei  navis  tnergi  debent  i  qood  failiu     tjt*  N«  M. 
id  Pfi  Di  A«  gravitas  poOderum  fingillatitti  fnmpco' 
tom  piajoreftC  A«  fiimprorom  cam  voltmiine  navii 
K«  A4  &  C«    Si  peties  tlavioi  eotifidersnror  foU.volti» 
Itiiiia  UgOi,  ferramentoyim  ^  dc  ponderum,  qOit>us  O^ 
iiefif or  tlavia j  eft  ^  fateor  ^  illis  re(poiidetii  voiQmeti  i« 
^«  (picifieeJcviusi     Scd  tiutem  fimol  «tetideoda  eiS 
Mfitas  nivis^  VOlomeOqOe  iftioi  Cavifatii  iddeiidulO 
filiqoo  tolomini  iiivis  ^  prios  coim  ^  quaifi  toti  iiivft 
HKr^refoir  |  de  lOcO  (oo  cjctorbandom  eflet  VOltimett 
iqotf  foQiondefii  ttoii  modo  diAia  poiideribus ,  (ed 
ctiatft  eaVititi*    iTaic  imcfil  Volomefi  cqot^  gravios  eil 
Hivi  fiifllpttf  tum  otlcrlbas  idjcftii  1  Oavis  itcque  mer« 
|i  MH  oibef4      Quomodo  OOnfirmitiolii  fitisfadcli» 
Mtti  I  cbondc  patcr# 


VL  A€Oi  t«ooii  liOfisMflfalitef  iiOpofiti  iqoii 
Aperoi^f  i  arqoi  vero  ceos  ilk  gravior  eft  pari  vote 
mttlO  li^di  i  orgo^  ^4  C4  hL  K<  io«  drca  icMt' 
Oqoii  ItlttatittOiOf  OodiqOO  eifbroiitor  catltas^  £0)01 
iMidon  ^oflcm  •(Firro  tiOtt  iti  protiotii  cfi  t  uf  exi^ 
iHnfiMi  ftfio  ctipcrimoi(o  tOtoprobiM^e^  Po^ro  tolo« 
•iM  iftt  I  01  toloiiiiai  iatitatii  eiforiDatii  fitiiol 


liter  grtvei   qtulre  actii  mergitloii  debet. 


VII^  Fftbit  Ar^icft «  fncct  k^rlKiniiti  ^  {kt  ^  &  dier 
lAiftruin  gNtiora  fiiiit  pari  veltiminc  aqu«^  nee  rftmeii^^ 
tncrgtititlir  ^  (ed  fingttlit  aqugt  niolecolit  innatant  % 
gravitas  ergo  tjibfi  «ft  catifla  inef^iioniii  ^tfpmietit 
aliqui :  it^terc^ere  lioc  ea(n  pirticulsrefn  caQifani ,  i 
quaj^r» fcindendntn  cffe^titatir*  togatl  3  qtarnam  fit^ 
canffii  ilk  partlcoiark  dAcien»  ^  m  dlnbltktie  fabartim^ 
^ccliari  &c>  miolecal*  poret  aqutfe  fubeant  ^  &  ift  iti 
iitfttneantttr  ^  r^pontint  i  notidam  convenire  iAteif 
fiiyac(ll  j  &  adhnc  fitb  )aA\tt  litem  eflfe*  Alii  eati^ 
iatti  eonilcntnt  iii  «ttllitakem  ^  i^  tennitatem  molecuk' 
tXM  divifiratn ,  quartlm  gravitat  tiiinime  (iifficietis  fij^ 
id  vin^endain  partiiim  Itttidoriim  coluKioiiem  ^  atit  te^' 
Itacitaccm4  Alii  deniqtie  in  mottim  inteftintim  pafi 
tinm  minimaromj  ^  qno  foblnde  immintito  ,  itit  prd. 
pe  evaflefctnte^  etiim  lirinims  mokculx  fiiUum  ^  fae- 
ebari  &€«  ad  fandnm  detaifeaflf  ^  ati  nempe  evenlra 
folet  aquli  eotofi  qodpiam  ciflQlt* 

VUt.  Avei  {fieeiiiee  gt^vidfei  fimt  eere^  t^ktit 
timen  1  (aftcfltiifltar  ab  aere  ^  fleque  urgente  gravitai« 
te  retpefttva  defiefldtffli  i  ergti^  %•  C.  t.p<  A«  D^  u 
t^olant  cemefl^  ^fopter  motam  ^  qaem  fibi  imprimonr^ 
(iiftinentiirmii  e^  cidflk  fortiter  ifert)eriti  ierit  C^  A^ 
volareflt  <  d  Itce  ebetfent  f4«  A«  &  C  iilt  tolare  011« 
priini  primo  (ibt  motnm  qaempiam  imprimit  ^  tttift 
eipinfii  aiit  fiirtiflime  aefem  verberat^  Sie  verberiw^ 
tot  aer  evtdtt  tiflqtf i  11^  iftaflattm  femm  ^  qoo  avit  Ci* 
fientitort  EtiiflHttte  ad  vdlattNfl  ivliim  C6llfifrt  ili^ 
inm ,  9l  ea«dc  ettianiio  ^  ie  ditatitio  ^  fic  enim  tnt» 
jat  volumefl  aerii  reCpofldet  leviffimli  oninino  pefl' 
itit.    Eodem  fere  mechaffifin«  enplicifldtim  ett^  qn^ 

homiiiet  (pieifiee  gttfiorce  vpk  iitflitem« 

t%. 


44t  StShtt,  CfmPBh 

tlL  Carpon  fpectfice  Icvton  fkpe  Miet^Hliir^ 
ftiii<iaitii  ergo  grAvi(«t  re{pcfiivanon.'.eft  caa^.mer^ 
fionisv        Pn  A.    Spongia,  frujElus  hortenfes^   panis^ 
lighofttiil  (egtnenMt  rrabcs   ifnino  &Cft  JeWora   (unt 
^ri  volamine  Mqnx,  Hrpe  timeti  tti^rgontar;.  cirgOk 
Cofifirm*  £xperientia  certum  habemQl  non  mtrgi  l» 
genam  vacaim  t  virro  confltum  ^  qvat  ciidem  fi  Huido 
Aqueo  repleatnr  i   cotitinuo  fondam  petit*       Eft  vcro 
kgeoa  aqoif  repleta  adiiac  I^^Ql^  pari  ¥ol(;minc  aqujr  | 
trgo*       Pn  91»  Volomen  ^qoit  re(pondetit  VOlatDini 
iblius  vitri  eft  gravias  vitro  (  aot  certe  i.  fi  levidB  eft^ 
debet  lagena  vacaa  adimam  dehi(cere).       Vo{otneil 
aqusB  rafpondens  volumini.  akerlus  aqo^  ligen^  con» 
&ii8t9  Kquo  gravc  eft  >   ergo  lagetia  tqois  replec%  le» 
Ifior  eft  parivolahiine  aqoopv  •  Msrg|tttr  tamcn^  proitl^ 
de.  qi.  N.  A»  ad  Pn  D»  A».SiSobi  lignea,  fru^i|8  horten^ 
(f  fi,  (pongia  &Ct  merguntur)  poftqdam  i^qua  per  poroi 
fiibeunta  in  locom  aeris  eva(eraot  graviora  C.  At  qadm> 
diu  intra  corporum  iftornm  poros  adhuc  latet  acr  K* 
A.  &  C.       M  Cmfirm.  C.  M.  N.  m.  ad  Pr.  K.  r i 
{>•  A*  Volomen  (biius  vitri  gravifis  e(i  pari  volamlne 
aqa^.  .      Qood  tamen  h^ ena  Vacita  non  mergdtdr  ^  • 
ttibocndam  eft  non  modo  vitro  ^  (M  &  «eri  lagenil 
caviufem  cxplenti  |  quoram  dooram  fimulfnmptBtmti 
Irolumen  lcvius  cft  pari  volamine  aqa«.       Sic  quidem 
facile  expcditar  objefiio  pr«(ens«  -    At  (i  vafi  vuri$ 
iubftitaator  vaa  liffmm^  cx(firgerc  vi4$1ri^^  oon  inQ* 
dica  difficultas« 

X.  Kihtt  immuiAtc  grnlirUatei  dtiti|clUt  ttiataM 
^gura  )am  mergitar ,  |am  (iui<)#  innattt  corpos  (bli* 
dam  \  ergo  non  gravitas  |  (cd  iigura  e(l  cauna  mers 
lionis.  Pft  A«>  Eadem  maflTa  plaoibi  (|>bsrram  cOti« 
ticaens  incrgi|ur|  cademqoc  iii  lAmellam  ca(a)  &  di» 
cloSlli  (bpernatar,  ergo*  l){»  D»  A<  Kihil  immutati 
gravitatc  abfitma  corpos  )am  mcrgitori  }am  (upcrua»' 

mC»  Af  ffHifica  % ^  ^  C«      Ad  iu 0.  A.  6io« 


t^ulul  in  laiiieiktn  didtia^ls  Inpdlrh^tiit  praptfr  immim 

nutam  gravitoiftvi  jpecificain  C.  Axaujfa  nova  figur^ 

Ni  A^  &  C.    Si  qoid  figutctribiatndum  tit ,  dicatur  ^ 

J^er^m^liceiti  occqfio  iiovim  dcgliifit^  gmititis  fpeci* 

£cx.  .  Sed  in  hoc  ipfb  diiucide  explicando  6ft  difii» 

tuitas.     Pars  ttnii  (ic  putant :  if»ivr  tjmfnodi  laminam 

Wcunqi^d  poUtftill  >  &  fluidui^  le  infitinat  aer  ;   undo 

lotutn  dggregatum  tx  aerd  ^  8c  lamina  (pcdanduiti  eft 

ceu  corpus  unutti  ^  tjnod  aa^a  iic  mdle  «vafit  (pecificii 

levius  Voluiii^ine  aquae  «xpeUtndo»       Pars  altera  iic 

Cxiftimant :  MaHa  globi  plumbii  in  lamellam  didu£ki 

folitarie  edti(idetanda  hon  eft »  (ed  cum  cWitate  ^  qufl» 

tirca  ipfam  undique  eftbrihatUlr  prius  ,  ^uam  tota  im<» 

ttiergatur  aquis.     Dicunt ;  obicrvatiohibus  &pe  adhi. 

bitis  exploratum  eflTe  ^  <}uOd  cik^^a  laminam  fluido  len* 

te  impoiitan^  aqli^  artoUahtUi^  undique  in  fpec'em  coU 

iiculorum  eath  dngehciuih  (  forte  ob  cohsiionem  ^  ^ 

lieque  taihen  ad  lamiham  defluaiht  (  Ut  fieri  videmut 

penes  vitfa    ifluido  abuhddhter  expleta )  ;    hinc ,  iftis 

.quidem  audotibhs )  promihehtia  illa  aqus  idep  prat* 

ftat  ^  tanquam  fi  lamin^  cihgeretur  lateribus  (bUdit 

Verticaliter  ere£lis  ad  inodicam  altitudinem  aflurgen« 

gentibus  ih  thodum  niivicui««      Sic  vero  facile  ex  t* 

lias  di6lis  cohjicituf  ratio  ^  ob  quath  lamina  plumbeA 

ftquin  inhatare  debeiit.     Dices  i  illud  eft  caufTa  mcrfio* 

inis,  quo  pdiito  kherguntuf ,  &  hoh  pofito  non  mer* 

guntur  eorpora  ^  led  pofita  figuta  e.  c.  fphderica  mec^ 

guhtur  corporay  noh  pofit^  non  dietguntur  ;   ergo» 

^.  illud  eft  caufltl  ^  quo  pofitd  ceu  ratione  formaii^ 

&  dired^  i  ^<^  ithinediata  ^^  thetguntur  corpora  C.  M» 

(ceu  conditioh6  ptsviii  iiid  obtinehdam  majorem  gravi« 

tatem  rpecificam  »  dut  ad  faciUus  fuperandam  refifteui» 

tiam  medii  N.  M^    Sic;  D«  m.  &  N.  C, 

XI-  Figurii  cft  cahfla  f^eleribris  ctefcenfuS  in  Ikt* 
dp  i  ergo  6c  merfiohis ;  nant  eadem ,  puto,  utriu(quii» 
jlAttflk  coDftUtti  debct.    ^r.  A,  mafla  fem  io  fphseraiti 


CoaCbi  celcrittt  AeCmdk^  qoaai  cadcm  tiHiflSi  fo  Ha        ^ 
fcain  fonnau;  crgo.      ^.  N.A*  adPr.  D«  A.  maffit  ^ 
fcrri  in  (^h^nram  coaQacclcriiisdc(cendit,  quia  majoc       t| 
«ft  graTittf  ^teifica  fphmntf  qoam  cabi  C.  A.  proptec 
l^goram  iphtfricam  Subdift*   pcr  acddcns,  qaatcnnt 
inatatt  cobi  figara  in  (phxram  mautor  gravitu  fycci'- 
fica  C«  h»  dircfic,  ac  pcr«ie  N.  A«  &  C.  qao  minaa 
voiamcn  qasdcm  aiicajas  mal&e ,  hoc  major  cft  gravU 
cas  (pccifica;  eil  vero  minas  volamen  ^hjtrs ,  quam 
cabi :  proinde  major  gravius  (p^ecifica  cjasdcm  malGe 
tfhznoM  j  qaam  cobiot;  hincitidcm  cclerior  de(ceii- 
taM*    sdo  :  Cabo  ferreo  re(pondct  major  (opcrficica 
finidi  dc  loco  (uo  dimovcndi «  atqoc  adco  major  rcfi- 
fientia ,  majorqae  firiflio^  a  qoa  denoo  repcti  poteft 
cardior  dc(<%o(iu. 

De  fluidis  e  vafe  profluentibus. 

%.  238«  Si  prcffid  ftuUi  aliqua  ex  paru 
toUitur )  vel  minuitur ,  movttur  fiuidum  in  eatn 
fartcm^  uH  pfrtjpo  fiAlata^  vcl  minutafuit.  Sem- 
per  enim  d<fici€nt$  virium  dquiUbritatc  habotur 
jnotxxs  fccundum  dctmftinationtm  vis  prMoJcntis  } 
crgo  u  prefiioni  prefiio  aequalisnon  refpon-' 
det  I  aut  omnino  fublata  fuit ,  feretur  hqut« 
dum  in  eam  partem  ^  ubi  preffio  fublata  mitf 
yel  minutat 

Scbol  Hinceft,  qaod  foramine  in  fando^  ant 
iatere  vafis  fa£^o  liqoida  crompunt ;  hinc  itcrairi,  qaod 
•qua  a(cendit»  fi  e  tabo  (iiperfidei  aqus  impoiito  ae* 
rem  exfugis ,  atque  ita  fvbj^Stfim  aqoc  portionem  ao» 

ris  prQjSioae  libcai^ 


\ 


■'^  De  fHotu  fikfJoruffis  4$t 

§.  2?9,  Cchritaf  fluidi  ex  todtm  vafc  frc^ 
jluefitis  eadem  efi  in  iiidcm  a  /upcrficic  Uauidi  di*  ' 
fiantiis^  divcrja  in  divcrjts*^  namceleritas  rc- 
fpondere  debet  preflloni  ,  ceu  effe^aus  yi , 
&  cwffss  fiiac ;  fcd  prefliones  in  fundum 
ejusdem  vafis  func  in  ratipne  altitu^inum 
f  §•  aaf.  CeroU.)  ;  fimiliter  ergq  celeritatei 
fluidorum  ex  eod^m  vafe  profluentium  erune 
in  ratione  altitudinum.  Altitudines  fluidB* 
rum  funt  difhntix  a  iuperficie ;  ergo« 

CoritU.  L  Si  vas,  c  quo  fluidum  crtimpit ,  flicrit 
<}0nAanter  pl^num  ,  fempcr  eadem  erit  altitudo  AnU 
di ;  quocirea  iempcr  eadeni  celer|taxe  fluidum  «rum* 
{>er« 

CorfiU,  IL    Etiam   cclerltas  fluldi  profluentis  o 

;     duobus  vafis  eaudem  bdim  habentibus  eadem   eft  in 

lEqualibus  a  ruperficlc  liquidi  didanriis  ,  diver^  in  di- 

verfis  ;    pofita  enim  atqualitate  bafium  preffion.es  ,  ac 

proinde  celeiiutes  Cmt  ki  ratione  dire^  altitudinuo& 

$.  240.  CfUritUet  fimdmrum  per  stqualm 
foramina ,  aut  lumina  erumpentiitm  Junt  utfluido^ 
rum  quantitatct  eodcm  tcmporo  effufa^  Hx  enita 
quantitates  fpedari  poflunt  inilar  cylindro<« 
rum  eaudem  bajlm  ifobentium^  qnorum  (ondica-* 
tes  funt  ut  alticudines  (perStcreom. ).  Porra 
motus  intra  foramina  tuberi  pofeft  pro  Xm 
quabili ;  cumque  in  motu  asquabili  Mleriio* 
tes  fint  ut  (patia  eodem  tempore  confe^a^ 
erunt  noilro  cafu  ut  cylindrorum  alpuidt* 
nes  I  b«  e. .  ut  quantitates  flaidorum  ^dem 

tevpora  eriUiipeatest  ^     .  /.;> 

Ffi  •       Spbfk 


46Q         mid  II  cspm  vtn. 

IIL  Etiam  fluidarum  imleeuUt  fi  nmtd^  traAom\ 
•tqne  iftad  dixi  alias  SeShne  hna.     Foteft   tameu  efi 
vaiidior  a9i0  vitri  in  fiuida ,  quam  fit  mutua  molecula^ 
Tum  fimda  compan&ntium  attraStia  inter  fe*      VeriHti 
bnic  cominonftranAje  revocabo  pbsnomenon  (tipra  ad. 
Icriptnm ;  fi  aqaa  p^r  iatus  externom  vitri  deflaat| 
(bbtnde  extremo  margini  adhj(ree  ,  gnttanqae  effoT- 
mat ,  quc  (enfioi  rucccdente  aqua  augetor ,  majcisqae 
fondus  ebtinet.    Sic  aoSa  non  conttnao  decidir,  (ed 
«bit  primom  in  formam  oblongc  (pharroidis,  tarn  ma- 
s      gis ,  m^hgisque  didndla  dtilribuirur  in  duas  velati  gno 
tas ,  auennato  qoodam  veiati  collo  fibi  coban-cnres ; 
qno  rapto  gattqla'  inferior  dccidit,  fuperior  antem 
extremo  margini  vitri  tenactter  adbseretf    Pntcm  yera 
delapfuram  eflc  &  alteram ,  quam  adhsrere  dixi^  gut« 
um ,  nifi  validior  elTet  atir^dio  vitri ,  quani  motQi 
flaidoram  intcr  (Cf 

IV.  Fortior^  ac  valiJior  ^  mutua  particulartm 
Miercurii  dttra&io  inter  fe  ,  quam  fit  attraQio  vitri  in    ' 
Jdtrcurium*     Iterum  obtervationes  ifthuc  accer£b  :  fi    | 
in8)orem  atiquam  Mercorii  guttam  leniter  admoveas    \ 
ininori  y  qnae  vitro  adbsret  y  Itatim  reIi6lo  vitro  com 
majore  coalefcit  in  anam;  quare  fortias  trahtturMer- 
cnrius  ab  homogeneis  particulis ,  quam  a  vitro.     ido 
Si  in  tabui^m  duos  fere  pedes  longum  ,  qui  tsmen 
^cfinat  in  tubatam  capillarem ,  immittatur  Mcrcarius, 
noneffltttt;  cfflait  autem  ,  at  primam  cutpistubuli 
Opiliaris  contingit  Mercurium  va(e  alid  contencam ; 
quod  rurfiim  argamento  cflTe  debet  :  validius  ^ahi 
Mercurium  tubo   iilo  contcntam  a  reliqao  extraneo      . 
lilcrcario  »  quam  a  vitro.       jtio  :  Mercariui  vitro 
mando  contentas  magis  urgetar  ver(iis  mediam,  quam 
«d  'vitri  parietes  ;    hinc  formam  convexam  induit ; 
N^      ijaod  profedo  futarum  non  cfTety  nifi  magis  trahere» 
«W  t  finuiaribas  parricuiis  ,  quam  a  vitro.     Cer^e  a- 

^  Qoai  w  ojppofito  migis  trahiitn<r  «  ritro  ^  con* 
'^  avim 


r 


t)(  mtu  fluid&runt.  ^6t 

tiiVtm  babet  fuperficiem^  t)icts  :  St  tninor  eft  «(♦ 
tra^io  vitri  ^  quam  iit  mUtOd  partjcuUruin  Mercurii « 
^uid  eft)  quod  gutca  Mercurii  vitro  iihpofita,  paiillti* 
lufti  complanetur  ^  In  refponfionem  funto  verba  P. 
JMako  !.  Ejus  fei  cauffa  nou  a  fila  i)it]ci  atfraSiofie  ai^ 
tifrjenda  efi^  fed  etiam  a  vi  mtitua  partium  MiTcuriL 
In  gutta  mimfingula  fuuda  vi  aquali  trabuntur  verfai 
ttntrum  i  Unae^  rotundittu  ejvs  exifiit^  At  citm  fUUm 
tla  quadam  vitro  applicantur  ^  ab  t^o  nonnibil  attta* 
imutttr  )  ac  proinde  non  urgentur  adcentrum  tanta  ef. 
^cacia ,  quanta  ex  adverfo  pofitd  ;  binc  piblata  aquilu 
britate  guttam  complanari  fieceffe  tfi  ,  puftQif  fupretnk 
'validius  in  centmm  contefidentibtis% 

V.  Mutua  particutarfm  aqud  attraflio  fMtjor  ndtf 
tfi  y  quam  qua  pofidus  ufiitts  gtttta  fafiifitare  poffit*  $i 
cnim  gutta  agus  fblido  cuivxs  adnarrens  fuccedente 
alia  portione  aqu2 ,  ifenfim  augeatur ,  majusque  pon<^ 
dus  obtineat  >  decidit  >  attra^lionem  tntttuam^  Vincco* 
te^vitate* 

VI;  Sed  nequt  AttraSio  vitri  major  efi ,  ^iftt 
^a  pofidus  Ufiitts  gutta  aquea  fuflinere  poffit.  Scili- 
cet :  etiam  gutta  aqu^  vitro  adhasvens  ^  fi  paululimi 
increvit)  6c  juftam  quandam  magnitudinem  adepta 
cft  >  induit  primuitt  oblongam  figuram  >  pofiea  de(er* 
to  vitro  delabitur.  Sic  plane  Vapores  aquei  (enfim  in 
guttam  majorem  concrffcentes  deflutinr  per  tabu^aa 
feneftrar.  jlt  iftquies :  ^i  attradio  vitri  itiajot  non  fir^ 
iquam  quoe  fiifficiat  gutts  uni  fiiftentand^ :  eadem  eric 
•dio  vitri  in  aquam  y  qU^  eft^aquse  in  partictilas  ho* 
mogeneas  i  nt  proinde  validior  non  ertt  afiio  Vitri  iil 
aquam  >  ^mm  fit  mutQa  particularotn  aqu«  attrafii^ 
jnter  (c  ;  quod  quemadmoduni  pugnet  cum  affertieu^ 
llhia ,  neme  non  inteliigit.  ]y«  validitatem  attr#4 
fiionis  non  modo  «flimandam  e(fc  a  quantitafe  corp^ 
irit  9xm&A  >  fcd  ctiaoi  a  tcnacitai^  >  ^ua  irafium  aditaj 

«  ctfcU 


^n 


4^4  ScahlL  CaptttVnU 

refcit  trihenti ;  tenacioi  autetn  tdhatret  gutta  nqoc^ 
titro ,  qnam  gottc  alteri  ^  at  iiipra  oflenfiim  eft  \uu 
mffin»  i  validios  «rgo  gotu  aquea  trahitur  a  vLtro , 
^oam  a  gocta  alia« 

yil*   ^o  ffu^ar  efl  fiiferficies  vitri  a^am  yir* 
flentantis ,  b^c  fnyvr  portuf  aqtut  a  vitr^  fit/nueri  po^ 
uft*    Obviom  expertmentom  veritatcm  evmcit  ;  De« 
fluat  majn&ula  aqus  gutta  per  externos  parietes  cylin,^ 
dri  Vitrei ;  detata  ad  extremos  margines  non  contiizoo 
&labetor ,  '(ed  per  bafiih  cjlindri  vitrei  difFoia  lerpet, 
sc  fiifiihebitur.       Fallor  vehementer  |  fi  alia  fiibeft 
canffii ,  quam ,  quod  ma;or  fit  (bperficies  baieos»  quam 
parietis  extranei ,  per  quem  gravior  aqux  gutta  deflu' 
xilTe  ponitor*     Itt/kres ;  majorem  aquc  guttam  pen« 
dere  pofie  ex  angnlo  vitri ,  qoam  e  reSto  latere;   qi^* 
)oremque  portionem  aquse  foftineri  poCTe  a  tubolo  an« 
goitiore)  qoam  a  plana  aliqua  vicri  (bperficie  ,  utro- 
€ique  enim  concurrunt  ^o«  veloti  (bpei*ficies  ad  unom 
idemquc  pondus  fuftinenduni ;  con^^irantibus  tecem 
viribus  iflajor  habetur  cfFeQus* 

VIII..   jittroBime  vitri  tten  modo  gutta  aqu£^ 
gut  fiuidi  alteriusfiiftineri  potefly  fidetiam ad altitttdif 
nem  quofnpiam  elevari.      Cape  denuo  cylindrum  vi- 
treum ,  (ed  cavum  ,  &  anguftum  ^  per  cujns  parietea 
cxtraneos  defluat  grandior  gutta  aque ;   difFundetor 
primum  per  extremos  msrgines  ;  tum  vero  traSa  4 
»ngulis  vitri  pondis  fibi  ut  maxime  vicinis,  6c  ad  fen* 
ibm  comiguis ,  per  internos  tubuli  parietes  afiarge^ 
€0  uique  ,  dum  vires  particolarom  vitrearum  aquam 
clevaatium  fint  in  sqnilibrio  cum  pondere  aqos  ele-       \ 
ratar.    Methodus  perquam  idonea  pharnomeno  expli- 
cando  {equens  eft  :  Cogitetnr  cylinder  vitreus  fefiione 
liorizontali  diftribui  in  plurimos  annulos  fibi  adoio- 
dum  vidnos  ,  &  (enfibiiiter  contiguos»    Aqua  deUra 
'  bafioi  cyliodci  trahiiur  g  vicioo  iOQDlo  primo^    > 


I 


t>4  mmfimdorum  4^^ 

tojus  ope,  6e  a£^ion«ad  .altitadibem  efltidehi  afliirgif^ 
quam  obtinet  annuUis  primu^ ;  efl:  vero  major  vis  ca^ 
jusvis  annuli  f  cujus  diamec^r  fitexigua)|  quam  pon- 
dus  aquae  eidem  re(p9iidens  &  proinde  aqua  a£lione 
flnnuli  idi  impulfa  tranfibit  a  iiho  ad  sduih  ,  a  ado 
ad  3tiuni ,  a  jtio  ad  /tum  &C. ,  dum  pondus  aquai 
^evats  adiequet  vin^,  du  clivam  anauli  fupremi ,'  % 
qno  fluidum  elevatum  fultinctur^ 

Video  eHe  hoe  loco»  quod  Tyronibus  dubitatia^ 

Aem  ingerere  poflit.     Eximam  (crupuium.^    ^*  qui 

,  tandem  ratione  eveniat  ^  ut  fiuidum  elftvatnm  ab  an- 

nulo  primo  tranleat  ad  adum  ;.  npn  enim  major  efle 

videtnr  a£lio  annuH  sdi,  quanvprimi^    quantumque 

annulus  fecundus  (blicitar  fluidum  ad  aicenftm  ,  tan^ 

tundem  primus  urget  ad  de(cenfui^  ,  aut  certe  Yiri<« 

bus  squaiibus  fluidiim  con{ervare  nititur ,  ac  fuftine- 

rt ;    nuUus  inique  haberi  poterit  tranfitus  a  imo  ad 

sdum*        ]^«  Major  equidem  non  e&  vis  abfotuta  an« 

nuli  (ecundi ,  quam  primi  ;   eft  tamen  maj(»  vis  re» 

JpeBiva  ,  quod  iic  intelledum  voio  ;  trahir  aimuluf 

primus  fluidum  (ibi  (iibjeduni  i  (ed  trahit  aliqua  vi« 

rium   parte  muiQatns»  pars  enim  impendenda  eftad 

iiiperandam  refiftentiam  fiuidi ,  ealta  cumprimis  ,  qus 

a  mutua  particiilarum  cohserentia ,  &  gravitatv  piofi^ 

ciCcitur  ;  qiiare  non  tota ,  &  abfoluta  vi  fua  irahit,  (ed 

mere  rejpe&iva.     Primum  annulum  excipiens  fecun* 

dus  iterum  partem  virium  exerere  debet  ad  vincendam 

actradionem  primi  ;   qua  elifi  viribus  refiddis  urget 

fluiduih  ad  afcenfum  ,   effedumque   fiium   fbrtituri 

Sic  deinceps  urgent  alii  poft  aiios ,  donec  annulus  ali<^ 

quis  fuperior,  &  fluida  elevatQ  proximus  fuflineat    ' 

tion  ^modo  tenuiffimam  illam  fluidi  iaminam  ,  quaml    , 

tontingit ,  fed  totum  cylindrum  aqueum  tuBo  angu* 

fiiore  contentum,       Nonnulli  fic  expiicant  :  tametfi   / 

fluidum  ad  fecundum  tubi  annulum  jam  fiiblatum  m 

pnmg  ceuhatiit «  flftcndit  ttuneo*    Cum  ^nim  amba 


I 


o 


.   4^4  Sfaktl  CfmPJtt. 

ki  tnndi  fiit  fibi  floida  cnpere  «qiiii  toiiaribot  lu- 
tafittur ,  annalornm  taincn  xqoaliam  ,  &  oppofica  ^* 
re^ionc  agcntiam  vircs  fe  £e  mntao  cUdant  ,  atqtd 
adco  tertioa  plenodi  cfieftom  confe^oitor)  fiuidoinqBtf 
attoiUti 

l)L  ASia  ifmmii^  vhri  n9n  pe^^tigit  ^   mfi  ^ 
tnhihna  inurvaUa»     LoHgtm  txfowrigisur  mum0  a^§t 
8io  aqiut.    Pars  ottaqoe  nttitor  txpcricntia  .:  fi  ^giiO 
temice  illito  affimdcs  gattam  a^s,  etqoe  vitram  pU^ 
Hom  qaam  proxime  admovcbis,  ver&s  illoJ  qiio4^ 
tnodo  affinrgct  aqua  |  Sc  adh^cbk.     Qood  fi  vitrofli 
non  prope  coiicinget  aqoam  ^  attradio  in  lenfiim  non 
eadct.    IL  Si  ptano  caipiain  afiabre  e3cpolit<l^  unpo* . 
tics  duas  guttas  aquc  roajote  intcrvalto  dlsjondaSf  CoIp  ; 
Jc(ccnt  in  onam ,  attra£lione  fcilicec  mtitaa  phsnOme^  ; 
tion  operante ;  iongios  itaqiie  petUnet  motna  aqas» 
irum  attraQio  -,  quam  ritrt.       Dicejf  •*  fi  ita  ell  :  nct 
quit  intcgra  aquz  gutu  a  modiqa  portione  vitrt  fii^  '; 
ftcntarl  )  non  enim  fitiguis  ^uidi  n^QleCQlst  yitruin 
<;ontingunh       ^.  Ni  Stqu.  qoantmnvis  fingola  gut» 
t9  puncJa  intra  {patium  attra£^ipnis  vitiii  Cta  non  fin^ 
iuibncri  nihilominus  ^  aot  elevaf l  pofiiMU.  Vi  motnc 
cohsrentis  ^  quia  partes  ultra  intervaUtim  'attralifndl 
vitri  poCt^  cohsrcnr  aliis  intra  illiid  coufiittitis*      Xn^ 
fcres  t  viitri   efficacitate  fuai  asiojii  ^.  uifi  tmuiffivMi 
quandam  tameUam  vitrd  contiguam  ^  ac  firoinde  iutrS 
jpatium  ipjius  virium  pofitam  j  reliqu^fimdi  t^ajfam 
*di8a  lameUa  cobn^entem  ra  ^,^a  auolUn  aiu$  fujfiimri 
^i  mutua tobetfionis*  ..... 

%^  Jla  fiuiium  fufiinendnm ,  ant  ehnaudum  i$    y 
wuh  anguftiore  fucceffive  ooncurrit  tota  imerior  tubuh^ 
rum  fuperficies,    Stibinde  tamcn  fola  vit  anuuli  fiifra 
fupremam  fluidi  fuperficiem  conflituti  totum  qyliudrum 
»qua  fufiefitat.      Veritas  prima  intelligicur  e»  JJfert^ 

yilt ;  altm  confcaarium  eii  4ffifrtim  IX.    Evio. 

tiCUfi 


'1 


De  inotu  fiuidorum^  .  4^$ 

•itur  ethtn  inde  ^  quod  ea  n)bi  portto ,  t]us  fluido  e- 
levato  jam  repleta  cft ,  nequit  ultra  quidquam  actrahc«* 
rc  ,  vel  clcvarc. 

Xr.  Si  tubi  angufltom  laBirtmfupremum  clmr^^ 
tur  j  aut  digito    ohftruofur  ,  flnidum '  noi^^  ^^JJ^*'gi^'i  &f ' 
cavitatem  tylindri  vitrei  non  explet^     Katio  eft  iri  aere 
intra  tubuH  cavitatcm  latcnte ,  qui  cum  de  tubulo  e* 
gredi  non  pofllt  ,    obnititur   fluido  trafto  ,    cjusqu»' 
afcenfum  impcdit ;    hinc  fl  tubus  hcrmetice  claiifiis 
acre  prius  evacuctur  ,  arcendit  fluidum  ;.  qufu  plera-i 
que  omnia    phtenomcna   pcrinde  eveniunt   iit   nacucf^ 
^ayleano^  «tqttc  acre  pleno.     Ipfum»  iftud  argumento' 
mffe  debet  s  ^uidi  afeenfionem  in  tubis  capillatibus  re-* 
peti  non  poflTe  ab  awtione  aeris« 


*•  ij> 


XI L  FitPum  fluida  non  itrkbit  vi  Jka  tota^  isT 
'mhfiluta ,  fed  ea  rantum  drfferentia  ,  qua  mntuamflui* 
di  attraSiionem  Juperat^  &'  gravitaum.  Nam  nnitiii^ 
Hla  attra£tio  ,  &  gravitts  fluidum' impedit ,  quo 'mi^ 
isns^.ifl  reiiqua  maffii  arelli  ,  &  contra  diredion^ni  at^' 
tradionis  terreftris  aflfQrgere  queat  ;  proindtqae  vi« 
trum  matuam  iftam  c6hs|rentiafn ,  &  gtavitatcm  priut 
fuperarcy  &  per  fluidi  reaSionem  altqua  parte  virium 

«  liiarum  muUWi  dehet ;  tura  execihi  reliquo  fluidum  e* 
levabit.  j^t  euim :  tantane  (it  attrabentis  vltri  tfHracita9|r 
utgravitatem,  &  vim  attra£livam  terrs  elidat?  £nimve« 
ro  fi  attradiones  proportionats (unt  maflis f  §.  163. )  » 
^ntum  non  infinitics  validiorem  eflTe  oportet  attracUp? 
iiem  terrz  ,  quam  vitri,  ^,  EiBcacitas  VMri  il 
minimis  diftantii^  applicati  validipr  eft ,  quam  tpj:rif^ 
cujos  attra£tio  omnis  cum  in  centrb  rcQdcre  concipi^mrl 
trabitur  fiuidum  in  ratione  reciproca  duplicata  difiantia« 

^     rum  a  centro ; .  nihil  autem  prohibet,  validiorem  efle  at« 

S  traftionem  vitri  in.minimis  diftantiis ;  nempe  arti^aQio* 
nes  ad  minioia  Infcrvalla  pertingcntes  non  (cquuntue 

,     iegcm  d«  raUpQc  rccifroca  dupUcau  ii&^uti^um.  , 


4€^  SOhn.  OfmVfSL 

Si  ril  tbeorenui  prflcieps  ytnaJyJis  ^ccuitt  ^  ptih 
cherrtinis  vertialtibtts  eroeiidis  lodt^^rJ-^  S^  Vtk  abfb» 
lara  vitrl  =3    Vi  vit  ab(blata  refiftentis  ilaidi  zzi    v  i 
crit  eitcdTtHr  viriiitil ,  qao  ^utrtm  pafttHHia  'diiri  pk 
#nnaioprHtu>iraliYt  fiibjtfaufn  fibi liqtitdaiii ^±3  9^^  '-Ht 
^^uutetii'T^fpe€iiytLtotim  Simmli  &abeu^'^  jj-  f^— *  0]- 
^  i^  Vd'^  vd  i  tunfr  c^m  fingal^  ejtadem  al4odi' 
iDoleeul2  trabant  ^aidufn,  toties  iunietida^eft  vvaiiFtniai* 
Aiva  vitri ,  quor  fiint  moleeois  vitram  compdti^tiMsl^' 
proinde  vis  re(peftiva  fingalarom  particnlariifin  <Iqg^'^' 
m  e(i  !n  rotam  peripheriam ,  aat  huic  proporciona- 
tam  diametrum  (prr  Gecm,^  ^  ^aaih  littcra  i^-Iapra 
defigiiavi. 

Stt  preterea  altitado  tubt,  ad  qaskm  flui(!c^'ajp 
furgic  z:  j4  ;  pondus  fluidi  ctevati  :=i  f.  Dl^)  lillaf :' 
fluidum  eo  u^ue  anbrgere,  dum  via  elciKana,  &>,pon« 
alus  Suidi  elevaci  fint^in  squilibrio  (^ferj^iit))^  b.  e« 


dhm  f  :=x  Vd  ^  vd.  £11  vero  pondus  fiuidi  effi- 
Vati  fp{e  cylinder  flttidus  tobo  contentus  ,^  49Fil  ^"'' 
ditas  invenitor  ba(im  eenitricem  diicenidoL  ih  aluFa^i. 
siem  (  fei(  Sfereom.  )  •      Baiis  liia  eirculus  eit ,  cagw^ 


I 


^  ;  ^  C^foJZ,  t  Inde  eroes  L  l%ui&p  edAm  i»  JSp^fi 
9ukff  -mgiffiiariivf ,  if  ^Hndritfs  jiffurgm  «^>y^  i 
MMfH  idfhudiuH  fim  in  rMQUe  r^^frtmidi^eiipf^mn^ 
A£(H9idunt  nempe ,  dum  F,  fto  -^^^  5»jiK4  4«  d^ifc 

^  V  qtiatititas  confians  (  cum  enimKjtallb^fi^^^vi)    | 
res  aiifiuloruiti  sqbalium  2cqufltes'ficlV^i^dirtfift6it«-    ^ 
^      lens  conAans  effe  debet )  ;   at  ps^iOM^V^^^i^^^vs^ i- 


1 


^^««MN^^m^  4K^ 


^. 


.     dfiTi  y  4«  divcr^;-  <^ri|iqU  «ftiua  iMlWf^fVj?a^i\ftqilite?,  ^ 

tOF^Wflkwl^  vjtri  in  fupcrfi^if ^*timiifW.jf«oIi|^i5/Pfeil} 
jl    «d:i3.^^dj  ««l^vationcw  iiciat  .Cf^jrf.  J,-.  ^     j- 1  ?. ,  .  •  ....  ..^ 

\       •, .;.  Wrofi,  jtl»   Fluida  div&rjt  g^^&pimPm^f^-, 
Jisa  ad  varias  tubuhrum   altituditm  yjf^ygnnt ^^f^i^iifjft,^ 
eiilm  diverfa  fluida  variis  tnodis  refiflant  ,  itidem  va> 


riaoi  cflr«  9fiortct  vim  attpllentem  F ^  vi    ttrqmde* 
c[M^  y^mm  nuidi  alccnuentis  alt^tuduiem.        ^ 


Tl 


non  fmdb  tn  tuhis  utcunque  anmjiis   nou  Attounutur  ^ 
Je4  i^tam  tufra  It&eihm  d^lnjcunt  j,  nam  (jiua  Mhgui* 
•di9f^^.acl|o  vitri  in  Merciirium  ^  quam  fir  'miitui. 
pj^rticular»m  Mercuril  attraftio  inter  fe  (  Aprf.*lV.  )  ^  ' 
cvadit  vis  retpeSiva  Vitri  quantitas  neeativa,  fcu  tnimr  ' 
fi/Ma  (  plane.ucijit  a  *.^  4  =:    *-*  5 ,  atquC  aqio  <^. 
iiihilb);  hinc^crcurius  &c.  non  fi)lum  nQi\^flbrgCri^ 
dcbct,  fcd  &  infra  libcUam  dchifcerc.        *^  ^    ^     ^^' 

i^'  N><!ir^.  ii^   j^imtiitaM  fiwdi   M  iivh^ytiibis 
tit^fmti  4U  pttfpue  Jiteifa  diametr^um ;  ac  |>rd!ti>-' 
d^  mii)ot"^  <|umi€0S  iluidi  elcvact  in  tubo  «mptiorev'' 
tjfinm  m  an^uftlore.     'Hoc  entm  ipfo\  q«<>d  Jlnidufii 
cc^  ttl^0i«(ia<tidai^  dwmaltitttdines  41^1  In  ratiotic  rccV 
proca  diamctrorum'(ZorciI/.  r.")j*fivc  dum  ^^  a  zH 

4.**M\9k\\W^:^fi{.:^:  ^d.  Eft.vcro  poiwjwj  fctt 
qnai^tj^  clcvii  j^r^i^d  ^iSwi^r^^Pis:  ,^DD  i  quart, 
fi.  quintitatcf  id^f ,ijg.|^  fi^  *  n»m«o  conferentur,  crit 


»■ 


4^8  Sf3klT,  C$Mf(lt 

siisdividendo per ^Dr; ai, ittQ^tqz^ Z>l^  Q.Ejl 
t)ices  t  fi  qQantitas  ftnidi  ^lcvaci  intjor  ft  in  cnbo  zm*  , 
pHore »  majoreai  efle  opof  cct  viin  tqi)^  aioplioris , ' 
^tnm  angnfti ;  prorhdeqae  alriiis  attoUi  debet  flnidttm 
in  ifto ,  qnam  fn  illo  ;\qQod  experientiflB  adver&tacv 
^.  majoreni  efle  oportet  vim  ^Jolumm  tiibi  amplio* 
r!s  C.  A.  tegfMvawi  N.  A.  &  C*  Annnloriifnr  vts 
cbfoluta  refponder  numero  punfkoruiB  a&nttic^  con(H- 
tuentium ,  qui  ts^jor  cnm  fit  in  «nuolia  amplioribuj^ 
quam  in  n^inut  amplis ,  major  ictdem  ^c  d^bet  vis 
mbfbluta.  At  n^eSiv»  pendet  a  majori  corvectine, 
qua  poilta  plures  vicri  particuke  tn  eandcm  .aqo^.por- 
tionem  agbre  /atque  adeo  majorem  io  ea  celeritaceoi 
efficere  poiiinr.  AnmiU  vero  anguftioris  major  eft 
curvedo ;  erg^o  •&  ikutm  vis  re^i^iv^9i>  Nentra ,  ta- 
inen  vis  carer  isfkOxi  (ibi  proprio  £  MH^:maJQr>abibld« 
ta  eievac  tnzjotQm  Omdi.qtfantitatem  i  vi^:imaj[or  re« 
Ipfc^iva  ininoremy  fc^  ad*mafdrem.i0/i^|^i>i4|^«  , 

Scboh  Ih  Jan»  prccipoa  rubttlAri]in(jC|i^l|a):Ujai 
plisncnncita  recenfebo.    Siint  fequciiici^^f /Jy^,^.  ^qs 
capillarii  utrinque  sperctis  aqi»  p^r&e  {^^^^ijj^  cop- 
tingdt,  afcendec  aqtuLsd.  »6.   \\mH,^^i^tr^^Jiy^apf* 
Immo  !  qua^cunque  pto&hdc-tttfbu^^tvfl^&inc^ 
niergatur  aquis ,  feinper  Si^asiKl  esD^ftJ^i^^hJincypi^ 
ahvtudinem  rapknnr  ukta  iib^<^::u\^r:^^Pl[^^^'V^^^' 
eft,  uthnn  aqua  talida  fit  ^  mj^i0^  p|ft^|j^f>X  j}j>- 
vi ,  aut  probe  deptirgati.aifhxl^a»r|Mff.|,:fen^ff  li^u}- 
dum  ad  eandem  altituddnicm 'iBurgift?)l^i:^u^ijjj^^^ 
'  dem  diaiHetri  ;  &'  fahric^i*    •Sio.Q(i%||&  pi^gppfiercca* 
randum   n6iV  eft",  ml  'tubojpum.-^tmfteg  y6»w^  %i^}»    ^ 
tnficd^  cum  hi^lmtu*  ibtfiilnis  ivitrflF^rifftfi^gf  a^t^  ^ 

notabiliter  diametf wi»  tnbi  «on^ft i^j^n?  ^Quyd  ^iff^     \ 
Stfirmius  adnotanrit »  aquam^Au  Wii^i^pfiiffijff^f^^Sjif 
ahira  afflirgire^ifi  i^memimiiimfiWi^  mgjjpichofn 
cft.     CrctHd«rim  ^  r  SmrMium^mhoiiM^^  tftis  fip» 
vos,  aac  nra  rlce  fcia),  escpurgacoi  ja  capiendlk  ek<» 


9i  mtu  fiitd^um,  4^9 

frerimentis  adhibuifTe.  Veto(hs  autem  liamori  com 
landa  tnttitiim  offich;  liquidocam  flfcenfui  ;  nam  ve« 
tuflis  tubis  ad  pdrietes   internos  plerumque  adhzret  « 

^rofhi  qucpiifm  inftar  a^rugiiiis  ,  quam  aer  (enfim  in» 
ducit  five  arrodendo  vitrQm",  &  folvendo  ialia^  e  qui^ 
|3us  vitfa  conflantur ,  five  aiiqaid  piiFticularum  terre* 
fttiam  6c  minei^lfamf  qaibuB  femperfeffrtpi.eft,  iU 
lihenido.     Derergicur  cruila  Ik^c  witri  a<^onem  iippe* 
dienS)  li  nfterior  tubulorxim  fispcrficies  (spiuji  tranC 
miflb  (ptritu  ?ini  probe  dilaator  » '&  ficcetur.    Aliat 
non  inutile  fuerir  tubos  foUibus  perflare,  cujus  audor 
cfl:  MufcbeHlfraL     III.   Utcuuqne  iof^i  fint  tubj,  mod^ 
carundem  diametri  sequales  fint,  idemil^idum,  ad  ean» 
dem  in  finguiis  aititudfnem  a^urgtt ;  &  vero  alTurge* 
re  debet ,  cum  annuH  a  fiuido  rem^tiores  vim  nulUm 
cxerant,  fluidamque  a  foiit  annulis  proximis,  quorum 
vis  pofita  diametrorum  (equalitate  cqualis  ed , .  eleve- 
car^  ac  fuftentexur.     MuJcJbeuirdkm  quldem  concra« 
riun/  ih  obtervaflTe  ^fHrmat.    Ai  mtgis  veritat^  mo- 
veor  y  quam  audpritate  Viri  alias  multum  cciebrati , 
>quem  tnhulfs 'iMf^alittm  hfmttim  ^  aut  cerre  tio»  orrt' 
iiino  cyliniricU  afum  futfle  puto.     Quidquid  Ct ,  iila 
MijfihenbrakH  obletvatip  adTerfatur    ob&rvationibui 
Mffinjferi  \  NoU^ti  ,  tf^eitkrednii  (  cujas  doarinam 
in  Cotntntntafik  fe$r9p«liimm  ad(criptam  hic  reces* 
ieo) ,    ali<»ramqtir'  ftiet tiff  moram    naturs  Icrutatp- 
rum.    Adverfttur'item'fationf  ,  cum.tuborum  intd 
Idngitudineffi  ftilaidorom  altitadines  nuila  haheatur 
propohioi  tumque' fluidum  in  eadem  fupra  tibellam 
altitadtne  confillit,'  fiu  tubm  fluidi  fiiperficiem  lam- 
fcat ,  five  pfoliMddias  immergatur  »  qua  immerfiono 
ajusdeih  tubMonfgittldinem  minui  necefl*e  e&     Keoi 
'  lot$m  fubinde  pervideric  laqdatus  AaSor ;    unde  in 
potlrema  editione  fba  mntatfle  ob  tobulorum  iongitu- 
dinem  altitudibij  mrqaam^CQmmennnit.      IV.  Diver* 
£i  fluidsf  ad  diverfim  altitudinem  clevantur*      Apud 
jUufQbtnhaJdim  viftar  tabelJa  exhibeni  rariam  iliami ' 

ag  f.  •     ,      alti.    •         # 


altiradiccff  »  qax  in  nibi>  4.U  Knw  ^ohgo, 

^iMMQ  I  iuv  ia  u;a:nccro  habeatc  xibcat)  fqi^  _.'  |]{m 

iubjkfto  ca  eti40i  dc  C4u0a  ,  nr  i^alim  lUt  ;  liqqoroji^ 

i^titadMi^s  non  refpaijd^e  gpuricanj^qil  ^CQiScis' ^,nff^ 

dcafiiAdbus. 


i.  ■•.•-.-  -'* 


ritHfi  Sfi«.  Aoijn;in..  •.    30,  vcl  3^1,  •*£.  It»,  V^ 


Oienai  viffii4l  •.    26,vcii3|.        ^    t.r.7f^ 

^qm  V.  --  -.    26,  .^    j.    I,.  Qc^ 

•  Oieam.'  lartiriipcij  dfeliq.. .    a j,  vcL  j4  .  : .    -^    i>3  V^ 

Spiriilllfl  »i;ri  <3iUub€ri  •. -  aq,      ; . r . . :      . -     ^kIN^ 

QteMm;«/W-.t.^r^bintJ^      IM^I  *R  ...       --    ^«#4 

.   ^kW  vjfH  purum, .        n     1 3,  vel  i  j     ..  ;^,  ^^^0,^8/^ 

V.  Flmda  i>ct!  cavitatepfi  tubuli  attolltintqr.fnora.je^ 
^iarda^)^  prjqciplo  afcenHis  funt 

Vnciores«     Niinlrum  :  iluidQ  (cn 
Bondus  clevandum  ,;  fc^nmque  plus  'virruin.i^effi^ 
.^  ;in  cawflp^eicyanrc^  gu«  dcmum  cunquc  iHafiCjjiSyb- 
inde^  cimi'p,(^ndus  cUvandurti  ex^quat  vlii^.  «t^itcn- 
tem  ,  exftin^uitur  omnis  celeritas  /  (PP^^QHftjff H&^ 

VI.  Ljquores  eicvari  pierumque.  indtiunt- rapremaai 
£iparjS£i<in  concavam.;    quod  Qr^iim«moreCI[i^potcfry 
tc  folet  9',  flnidorun>.  mol(?.cuIas  magisj  t;ra^fii  iMgfl 
quam,  ^  ic  invjcein»     Dixi  r;;/m/^/jf^^,  m^ 
rius,  for.mam  convexam  induit.  "^     yTJ.  |^^  Jt^^W;^^ 
fui  exfrcijiitatc  hermetice  clau&s ,.  nequc^prjM  ^agrc 
«vacuajus^.  fyprit^rion  affurget  %ijydiiHn';,  p|j'p^^ 
icilicct  a<irc ,  qui  elafticirare   fo^  Vini  comnrii^^i\(^ 
elidit,       VAU\    Si  tubus 'debita  Siii^i  .<C9PU Jfj^y^W* 
flus.  ic;ife  eclucatur,&  Hquidi  fiinerficieni  dietejrcrs^Jp- 
ci^iat,  lubiidere  videbuui:  nuidtiift  \  tubo  cnimHUtiF 

'  •  coni 


J 


11» 


,  coni^iijtis^jMii  adWe(cit  gtuu  «ngent  pondat  c&i 
lumns  Cttbo  indufs)^  Siqae  tubas  c,  fltiido  pehitui 
'  eximetur  y  redibic  iiqnor  aa  cdnfiicftam  alticudi^em^ 
tum  iqimotus  l^rebit  ;  nairi  fida-et  ieparationt  co» 
2ias  y  queW  dixi,  abrttinpitar.  IX«  In  tilAo  !tfcli» 
lUCQ  fluidam  rapicur  ad  eam  altitudinem  pi^rpthdku* 
larem ,  qnc  kabetur  in  redo  ejusdem  diametl-i ;  fci* 
Hcec:  in  tubo  indinatd  non  renftic  nifi\gVavitas  re» 
AcHiva,  'm  re£to  abfoluta*^  majorem  igitur  .fluidi  por« 
tiOiiem'  attollere  debet  vis  quaecutique  elrirftns  in  tubo 
ihdlnaco,  quaih  inre£lo.,  X.  'Situbittf cytindTicus 
'^uido  fibi  debito  jam  expietus  invertdttif ,  deieecidLt 
iiqu^br  ad  oppoficum  tubi  labrum  ^  in  quo  ad  %iitiAefa 
iQcicadinem  futpendicur  ,  ad  qu&m^rtte' teuftui  fdit« 
^^L  Si  cuboruih  parieces  febo,  cei^  ffifii^  aut  t>leo 
illinencor ,  nultus  erit^  fluidoruin  |)ilerorumqae  iicen- 

-^  "^^s.     Si  lacus  danciDcat^nam  hecei^c^cMed^iftiusmodi 
cbr^oreobducecuif;ifl{i^genc  flnidaf  per  iatuis 'Ureriim<,  ^ 
]>citi6  Mtrcarium ,  tujus  fbperficies  boc  <M(b  in  «i^co 

^  pUicudinis  concava  cric ;  manifefto  ^  nifi  fallor  ^  indl- 

,^  4ii<^^i  Ihagis  crahi  ^tefcur'^um  a  febo\  vel  cera  ^c« 
^uam  «  vicro.^    XII.  In  vacuo  Boyleaho  ^adem  propo 

''|>iiiaenomena  locum  liabenc ,  qus  ^ere  plenO  ;    nifi 


qrtim  trahi  ppjpiiK, 

' ^'^'^^^^^ihlpitt  Stiperaf  phacnomenoram  canffiim  do- 

'  fmir<^;  quod  priusquam  facio  ,  nonnulias  Phyficorona 

'oMn1on6s  retitace  placet,  ac  refellere.    L  Sunc,  qui 

'  'ft&entafta  'fluiabrum  iti  cubis  capillaribus  repecanc  ab 

iiUtquitt  prejfiofie  Mrit,     Sic  pucanct  Incernus  aer  ae» 

qtte  libere  hoh  floic  ^  I^  nec  fluere  peteft  ifitra  tuhtm 

'  m  adfmium  attmflps  ^  acque  eKCemas  \  quare  ejosdem 

«quinhriam  cdih  externo  coHt  necefle  eft.     Hoc  fob« 

litd  yaltdius  ttci'^aV|iremQntar  flaidi  tb  «fcc  cxtcrno^ 

Gg  4      ■      .    '      '     it'. 


-A 


,^  a]b  eQ.  it  rfi1>in6s  capilkres  ndigBfinir^.  IL  Alii  )rf 

folciMttu  ilium  ajLcrim  Juum  confqfgioni ,  eaafHaiaii- 
les  ;,  fupcills  huji}^  .loaceri^  prdlioncoi  iotcr  tQboram  / 
«ngurilas  longe  "ihinorenf  cfle  ^  quam.  in  cxterno  ni<''  I 
\)oruai  ainb/ru  ;  hinc  rero  fluida  fublcvari  dican»  ob   | 
'^iBaj(>feiti  stherif  excerni  efficackm.      III.    Ooniml»    j 
Dircuntur  alli  ;  •  ilUrft  fobom.  dhiiHm  pt^jjumdm  sttnom 
fib€r^  ,  ac  protnde  aer^m  in  poris  fluidi  hCBnccm  Ji 
fxpihfdeff^j  eoq^ic  paflo  ^idwi  uratri  ^ad  ^Gxnfuqh 
Tria  hxc  ^mpi^i  pfopc  'n  idem  rectdunt.      IV»    Fk-     i 
^uic  oonnullii^  cdufTam  jj^c^fun^ere  in  aliqoam  ,  nefcio     j 
quam\  imongrucntiatn  y  quae  irirer  aerem  ,  &  virram-    i 
iiirercedat';  unde  Hcri  alunt,  nt  aer  hon  tam  ar6lc\in«    I 
tefnisVitri  paricfibos  adhai-cat,  ac  fiqui^om,  idceqoe    ^ 
'ejui  prejji»  mmtiamt^      Porro  incongraenrMoi  illam      : 
pruiiciici  rokint  rel  ab  Ikterogeuek  ^ihrathmibm  aerif,    '■ 
cT  vtfri ;  yoX^^tnaurii^Jubtiiiyqrxx  aeren»  intcr».  4     ' 
yitrum  torrenris  inAar  ie  ^midat,  &  \sX\iAox^,tLi* 
hsUonein  impectiat :  vel  denique  a.  dillimiiiitis  afn^ 
jpb(trmts  aerif  ,  cT  i;/rr/j  qq^  Hivicem  permilceri .  fit- 
queant;  cum  6x  bppofito  atm6(pKaEruTa'fluiai*,  *&  Vi» 
tri,  at  primum  ahcra  a/teram  contmgttV^oaft^iftTi- 
tiam  coaiefcant,  cor^oraqne  cohjungamur.'    V.  -'QtM» 
'  busdani  viram  cA  rcubulonun  capilhdsilit  pfaaDfutifi^ 

na  pendere  «h  cadem  adIiaK(i6no^^iii^Qiiif1t;(it$l  iftl^ 
interna  vitri^  Sed  auteip  lic  mcnreti^  fu^fn  ^pliciini^ ; 
-  fluida  virro  adhsrentia  partein  pond^ris  .(\u]ainitt^ 
(aliquatenus  enim  fuAenranttJit  a  virroi4f,.«0.  pfop^^ 
rea  a  vfcinis '  ejusdeni  fluidi  cblumhi^  Ultt^ 'Wemih 
prorriidrdcbeht.  •  VI.  AKi  aivocahc^^tiidaAj  qjJbd- 
dam  eloancnm,  cujiis  ope^liqtjida  cley^nNit?' j  ft^^rt- 
Jt^mtm  pleriquc  y  caof^  ona  itdii  cdmMiti-^.flurcl  I 
tjiant  ad  eun^Um  effciimn.^cpHQiirirerfi; .  •  '  :. 


xS«  ^SOf  In^qwUs  friffio  4grii ^^^^dkrii 
(fquac  mof e  cjitnfingicur)  fattft  nm  tfi  ^cmfas 

fiui' 


1 


Jik  motti  fiuidorum.  473 

\         Jlui^rum  in  tuUt  iapiUi^r^uf^  "^Pr.  p»  I*  dd  amH^ 

^tpeH^^ns  :  Iri  Viicao  Boyfeaiio  p«rinde  ittlhrgrt 
fliiidum  ultra  lit^clUni.^.atqae^er^  plenp -j 

crgo  tMquatiur  frme^l  arr  caa04^non  c^^ 
a/cenifus  fluidprqrp»  IL  Si ,  Mr  juc(;uaqu0 
premens  ik,  caafla  pbknosneni »  debot  .fluK- 
dum  ^secifice  kvitts  altius  aitoUiy  qaam 
gravius  j  non  autem  aithifi-  atfollitur ;  fic  Al* 
ci^bol  vinit  fiuidSrum  leyiffimis  accenfSndlim^ 
adurgit  folum  ad  18  >  vel  l^,  iineas ;  OUum 
vttrioH^  admodum  grave  >  prope  26»  vel  Tji 
ergo«  IIL  Aer  a^que  den/iis.  eft  extra  tu. 
bum )  ac  in  tubo ;  quomodo  preffio  aeris 
extemi  praevaleat  ?  IV,  Aer  infra  tabnlos 
ii^tcunqueanguftos  eadem  libertat^  fluit^  qua 
extra  eosdcm.  TeftiS  mihl  eH  '  Bliljffingerus  ^ 
qiii  in  Barometro  yafculum  flagnahtis  Mtr-» 
c^irii  in  tubum  capilUrem  definere  fecic,  e<« 
a^quq  Mercurii  mutationes  advertiti  qualee 
vaicuio  magi.s  pat^nte  fiebant  alibi  ;  quo 
N  quidejti  eveato  liberrimus  aeris  fluxas  mani« 
fefte  comppobatur«  Siffn$ntum  ita^e  ij^  vt^ 
itqUdif  prt^o  airiu  ABverfarii  hoc  txperi^* 
mento  mi(^re  t^rquentur;  K\t\c  argumentum 
Crwi/^dicijfo|et,  Pr,  p,  11.  fertimnf  ad Mbej* 
rtm^  £x,^Ufn^enti«ra43verfaribrum  «ther  li^ 
ber#  perv^iiit  por^^  omAium  corporiam ;  er-k 
go  fitnilieer  iibere*  fluit  per  ofHum  ySl  cavi* 
tatem  tubi  qaamuRivts  angaftiffimi.  Qciid<^ 
T\\  igicur  xqualiteir  premat  xther  intra  ti^*' 
bum  centenids  com  exteitia?  II.  Dabo  In^ 
terea  UberaiiteF:  inxquatem  eife  preflioneai 

Gg  $  ^        «the--       j 


•474  SiSi*  If.  Oput  Fni 

9 

« 

.«therU  iiiteriii » &;  ei^tprni  j  qvi^  atnen  eftft 

qood  fiq  uida  g ra viora  alttta  Aoroi  Us  lar^g  iMai      j 

*  teviora-  ?    qaid  ,  qiiod  niperfidcfap  l^ercqrii    A 

cdcTaTi  coftreu  fic  ^  aliortmi  liquidoroin  i^e  ^  J 

coflcava?  .     -  <         1 

5c;i(ofL  Pfponerc  (olent  Inso  :  Aer  extra.  taBum 
.^flpiliareoi.  ifitus  gravU  e(^ »  &.  flaiclQin  {ibi  fQb^eduox 
premic  ;    poteft  itaquc  fluidorain  afccnfas  |>ro(icUct 
jib  acre  preroente»    li.  Mercurius  ihBarometrO  lUsro 
JibeUaiQ  ^Uvatuir  ei^  cauira  p^rementis  aeris  ;  {\mi\\ttg 
S^t^  flntdiMi]  iii  tubis  capiilaribus»    Ilt.  In  tubis  coin- 
g  mi^icaptibus  ^icenfu^  iluidoruai  ad  Ubellam  tribuilto? 
..viribusjpreni/^tibqs  i^  qqidni  etiam  tribnator  iii  ^nlo 
pipiila  ci  ai^ennis^  ult^a  libeiiam  ?    i V.  Noii  po teOL  mt- 
.  sior  .efle  edicacitaj^  aeris  itr  aqium  per..tuI>Qs  *^rcgio 
w  Taftos  ajttojl^adam  ,   quao:  per  tubos  'ca|iitiaces  ;^  iu 
follitnr  .aHCCfi^  per  .tubos  ufcunqne  vaftos  Y^J!^f/^f^ 
M$ru  (  qwd  psiut  fftOfitlm  ffydr^ulkif);  ergo^^fier 
tabos  cap^Urea»    V*  £orundejn  efFe^ujim  eia^d^^eC 
(c  debfffjt^CfmjPl^  ;  yro^ide  fi  aUqiiiaa/cenfus  'ultc^ai« 
teifam  tribuendus  efl:  preflioni  aerla  ^.  tribai^. f^ebjeot 
omnes.      Confimu  Simiies  effedus  ,  quamvis  'aliqua 
partedilqrepajit^  refundendi^o^^nii^t  V^  aiiap  caoC 
Jkai^  j  fed  circnmftantias ;  ^rgp^^  YI*  ^'^f^ftJ^TOJI?" 
,iifea  in  .t'ubis  communieantibul  (^  qon^ponpjp'^  fl^^Ml* 
'Silh/iii  cx  pau(Gi  aqtiald^  preflSonis;;   xrga  Anjl^^ 
tuba  capiilari.  aflfnrget  uitra  liiellkm  9X  ckv^jn' 
Uur  prj^mentji  aeriil  interni ,  ^coKrerni.^  \yi 
f  qri  acr  e:i;tertw  spqnalicer  non  premit  cyBi*J^j[^jfp;^ 

4um  i|li%  quidem  corpo^a  mtttoani'  idyetupt:  ^^r^^;/- 
wm  K  r  ^  .aqna ,  &  vitr um  :  aiia  w^j^fl^i^^f^.t  ^^ 
ter,^  ^  yicrum ;  qi^pcirca  fuperandiaefaui^^iip^^^^^ 
lU»  Hnpendi  dpbet  yis  aliqua  aeri^  (bpremd  .j^jipj^i 
^a  tecmmbeotis  ;  eom  interea  aer  \e;Kterous  %o^  fi 
^MijpfQniat  j^^        flifldupi »  ftaiUnie^  i|^ 


I 


^nm  iiSMt  ^fSvtm  ^qhim  ckvcc  ^  hb  tiki^nkfn^  Mi. 
^  ^^ul&  «(yhkrmkiiri  o«ii|  fkro.  ^  VIIL.'  mikm  im^ 
qnlisr^reffioL  hider  Dafci  poitef|  ,1  qvCKl  Aei^>ciit«»Mr 

iriter»  omniqiie  ex  partc  urgeat  liqaiduqi^^Aerjy^qre 
t^ulo  contentus  preinir  liquiduin  initar  com^  ipdim- 

2ue. non  attingit, nifl  eaparte^ qua coni^s ip  apicem  de* 
nlc ;  jrimdr  itaguc  crtc'  ddbdt  prelSb  ircr?$'interni ; 
';qiMrti'  externl  i/^fic  Honorgm  FIAfy  y  Hfuriniiis  Stc^ 
tK*'  Si  tubolas  duos,  trcsrc  pddes  lon|;us  hi  viu;uo 
"  Boyteanb  immergatur ,  ^afcender  aqua  tiSri  }ibcU«i|i. 
Siqofe  poffea  auxilio  n[iac)xinxpiitvn4aticse  ;<iibito  irau 
Wt^aturacrv  ad  majorcm  tltittidinchi  afTnrget'aquftft 
"^  Atqui  vcro  iftad'  futut^um  noh  cft",  niG  mmor  fk  acrit 
'|>reifio  in  (lipreipum  tubtrfi  bftium',  quanii  jri  aqnam 
va(c  comdiram ;  crgo.'     'Cdiifii^fh,  Si  ab  ^i^rlr  prc(fi6« 
nd  i^pctcndu^'  ^ft^  alc^Affls .  alt?dr ;    cur^  rioir  afccnChi 
jprimus  t^^(^z  ik^xiii  aj^htjks  fi  X.  Af 

YaiVem  ytTier  'o^teirnHsIftfa^il  ^rcmttyqiiam  interdtiSi' 
li«m  cxtdrnu^  tiberc  ^ircmit ;  Ititcrniu  vero  licet  pcr<» 
;ihi^at' pbi^o^  '^ubuli  /  at  pcrvaiclere  hequH-partct  ibfi« 
das^  mnjO  cxtenio  nizpx  crit  1i>en«l  ''S^^^^^x  ^^91 

'ihurbo  V  ptoifadei  -  .  •      ' 

' '       *».  acl  t  t>.!  A  ' ACir  cxtraHeuf  grsfSlr  ^ ,  flc  Ai< 

'(^«ift'  ffl)t  fubjedlluq  piei^ir-,  fimul  tam^n  ;'&  ici^jf 

j^preiint  a0r  imermii  tubd  cbntentusCi  A.  non-premH' 

f^alite/^i^.A.    D,  C.  potcft  crgo  fluidorbm  alcch^ 

Jijis  ^roflcifti  ab  icrc  cxtfan^o  premcutc,  S'm»if«<* 

"mn  k'^i  /e^ffitC.  C.  fi  aque  rtf/f/toN.C.  videph*n 

noifnetaoftVlC    Ad  lj[.  C  A.  N.C.  In  (ummitare  Bi* 

iron»et|d  babctur  vaeuim  TorrictUi^num ,  ac  proind^ 

hihiV^lV*  qtibi}  afccnfiim^Mercurii  prohiberc  poffitji 

.  au^  idibcdHrc  ;  debet  itaqoc^aer  cxternus  va(cula  fi^ 

gnaitti^  Mciciirif  iiicuinbens  cfFciftain   {uom  (brHrin 

^At  in  lubisf  Vifeyjdcibus  tantnndem  frentit  a&  ixm^ 

m ,  5j»ifirf«wtt'^fein^«tf.,''v  idcQ  cxt&nosi  ptft^ 


A 


47^  SfSioIL  O^tVK^ 

T^ler^  nM  pocdl ;  ergol     Ad  III.  C  A.  N.  &  Si  M? 
qQiddbomogie^ipa  in  tubis  ^pmfnanicaiidbus  ad  tanl 
dofn  alttradin«ai  aoq  aflMrgpu^ ,  non  habemc  arqQiii* 
briras  yirtuiD  pr^m^ntium  ^  ergo  aG^nis  ficri  debe| 
leciindunr  deternuiiatioxiem  vis  prariralenijis.     Semper 
«iit«in  babaxui:  «qualicas.virifim  .in  tubia  ca{>iilartbu9| 
li.e.  aer  tnfernus  sque  premit^  ac  externus  ;    ergo. 
Ad  1V«  P«A..non  poteft.mLnor  effe  vis^  4(  e^caci« 
tal  aeril  >  (i  vis  otrpbiqi^  fit  expedita  C«  A.  ii  impe* 
dita  N«  A»  £c  C«  per  tubos  utcunque  vaftos  attollituc 
.#q«ia-  w  frfrmfftui  aeris  ^  (i  aUus   tqbo  copteotus  aei 
«Tcei^fum  nm  impediat.     Impedit  autem  in  tubis  ca« 
pillaribus;   «rgo  in  tdii'  aqua  non  attoIUtiu:  'ut  frt* 
menw  a$rv.    Ad  V.  Eortindem  efie£^uum  in  ^^inm 
$ir€um/imrii0  pofitorum  ex^em  (unt,  caoflse  C.fyi,  ii 
divtrfis  fofi^rum  Subdifi,  f\  cauOie  in.diver(i|  cire^m* 
fllintiis  ^ifuditer  applkari  poflint.C^  A,.  (tcx^i^,,f^^ 
&  C»     Qjaii  y  nifi  ineptuay  fic  arguat ;  '(^nsp .  trS^o^^ 
tor  arftos  maria  ,  ac  proinde  a(cen(us;aqUarttpi!  $narin.a^ 
mm  ;  ergp  &  aKceiifas  in  machinis  HydraMlicui ,,  vct 
rubis  capjlkribui*    Atqui  nqn  ovum  pvo  iimilitis  .fiL 
Quam  drgumentAtia  ifta  alteH,     Ad^Co^^irm.'  ^yo  ;!.ef- 
£s3uutn  dtverfitAtem  refundqndam  «fTe^iii  circjiip^n* 
tias,  fi  diverfitai  mero  fic  ^uxidetmria  ^  qua^ /alternif 
modo  obtincat^  modo  non  qhtioe^»     ^  coii/Jfqni  fi 
fuerit,  in  aliam  caufTam  eiVconiiqep^*»     A(^  .y|w'C. 
A.  N.  G.  prccario  iiimitur  inaequalis  ifta  prfcitia     Ad 
VII.  N.  A(  Qaod  de  congruentia  adjicitur,  fatfi0imui« 
id  quidem  e(f ,  vaniilimom  ingeni!  fIo6\iknt  iSgmen- 
mm  eft.    Nam  ^unde ,  oro ,  'probata  ^bttiii^^l^^»  eis^ 
llentta  ?    Quid  ,  qudd:  if$  byf^efi' cofigrueHtM'  tftmtf 
non  (atti  expediantur  piecaque  phaBaomesff  ?.  r{Ufi# 
«erte  nequit  ?  qoomodo  ercceCui.  Ani^t^fo  y^yv^ 
capiliarilnia  mifiime  con^entifnt  l^gibt^s  Hjrdroft^tici^. 
Accedits  quod  eadem  incQngruentia  ^  ^^u^  liberu^ 
i^is  ingreffurii  io  tuboi  iinpedire  dicitur  ,  (imilitet 
Aiipedire  deltear  libehini  cgMrum.     Ad  VIII.  -  N.  A. 

etiam 


i>0  mm  fimdcfumi  477 

ktim,  ilJud  pro  lubidinc  fingitBr,  Gont  iftl'  0ec  Wi 
byp^tbefis  fuitincri  pofliint ;  inde  enim  dartflimd  con- 
fccudbnc  ciicio  :  boc  major^tn  cflc  dcbcre  clcvationeni 
fiuidi ,  t[Uo  rninor  cdriulus  aercus  aplce  ftxb  tubis  in« 
cumblt ;  q&od  i-epii^nat  cxpeHnfiento*  Biilffitfgeri',  tjni 
fumpto  tubuto^  cujos' ItJrtren  ab 'una  citwemftatb  ki 
aliam4dentidem  mimiebatdr  ,(C(Hnpcrit  Auidum' cleva/* 
ri  ad  eandem  altitudinem^  quacunqtte  exH^emitate  to^ 
bus  aquis  immcrfiis  fuerit ,  modo '  ftmpcr  aiquc  proi 
funde.  Quis  autem  non  vidcdt , '  majoretn  conum  ha*. 
6cri  ea  parte,  qua  tubns  divcrgit ,  quam  ulSi  conTieri; 
g?t  ?  groind cquantum vis  major  •,  minorve  conus  ttii 
bo  iiACumbat  ,  nihiloniinus  fhiidutti  adeandem  tltita# 
dinem  aflurgft ;  crgo.  Ad  !X.  di<?b  :  phienbmefii 
cauflam  in  eo  efle ,  quod  acr  hnmJffes  ,  &  iiicccflive 
campanam  ing^rediehs  pricis  agit  i^n  vldna^^  «quam 
()remen4a ,'  qnam  per  fbprcmum  *  tubuli  oftium  in« 
grediatur  ;  binc  dencientc  ^re^iiterno  fluMum  akyi^ 
iur. '  Subitide  camen ,  «ere  )am  undtque  ptv  campa* 
nam  difiiliS)  ,  redft  Ifquor  ad  priorem  altitndidem. 
N6n  iraque  mhior^  am  iitiequal^  preffio  aeris  Tliterni 
cauflaefl;  clevati  fltifdi,  ftd  defkBus  omnisfr^ouis  in 
tubo  exci^cnd^.-  Satis  j«m  liquet  refpon&o  ai  Confirm^ 
Ad  X.  Nf.A.  ir*«tfier  oninis  aptuseit  ad  pet^adcndoa 
|lorqf  :c^jusque  cok^rh^  ntfm  ineptui  wUeri  potelk 
a4  io&etnldum  >flt^m  tobi  ? 

j$.  2^S  T*  £Uv^iQ  fiuidorum  uJtra  liUUm  trtm 
tm  n^^^Mi  .4ifnin^  freffioni  Mmofpbera^  (^  ix 
0m  Mta.Mpntnfi^ni  lurii  in  fimdo  laiintit^  Ndin^ 
iMmmu(^  iq^enr  illa  oommenutia  oftt  11% 
Ftuida  ^' aert  iprdlie  depcurgtttii  etiam  altiiK 
dfcenc^utiV  Qjbdn\  XIL  ) .  IH.  In  liquoribai 
calidis  diJlJQr/eft' aeris  explrcacio  ^  quam  19 

ft\g\d\^^/f^  umen  1)1  altms  a&enduD(| 

"     "     .  qua» 


47S,  Sem»  II  O^  f}ff^ 

iea  non  ;   quid  igitur^  guod  m  febo  iltftia^. 
non  elevatur  fluiduni  l    Obfunc  etiam  phx- 
n^msflf  Mcrcuui,  wc  flaRoi  liquap. 

£.' 2<2.    /n  m^j^freffl  taM^entUm  squfi,' 

n  rtjundi  non  dthet  4(cenfux,  \ 

Proh,  Etiam  cofigrpBntiW,, 

j  negu6  nafci  p^t^ft  «,  V(«'' 

Vj  quarum  origo.iDechar-, 

t  exponltur ,  CHnimatirj^"^ 

m  fiuidorum  undigHe.preT !. 

^  promde^e  yibrationcK,;^ 

:'}  DCG  aJubttU.maiiriA\\iri^ 

tm  fluentej  cur'emin,pc^, 

fiiniliter  fluat  vitrum  inter,  &  aqu;Mii  if  i^-.t 

que  a  diJ^miUhut  aerii ,   ^  vhri  atmhjpkafkk  ; 

qua  Cur  mnruo  permifceri  nequeant  ,_,l]ap^,^ 

«flequor.    II.  Non  minus  tenaciter  i[itVqacI-,,> 

haeret  aer ,  quam  aqua.    Tcftem  apgello  ^^^^ 

iWak^  t   Capt  Cdo  verba  Viri  fblertiflinujl  iu^unf^ 

tres  poUieti  longUfn^  diamtri  ^  Unearuml  fi^.tfUft- 

aqua  ajfurgu  ad20.  Hneaj^  tundem,  de  a^^a^i^  .- 

num  injltSt,  dum  aqua  verfui  'mediutn  ttihi  j^O'. 

grediini  atri  locum  rtlinquat.     AppUca  in  hoc  jtt^,.  * 

rurjue  aqux  tubum ,  afcendet  ea  denuo  ,  huUamque' 

tterit  iniirtJudet'    Edulio  tuho  ^  atijui  ad.pnptn' 

diculum  eonffjlinte  omnis  pene  a^ua  it^rior  ^utf,, 

t^ue  ad  abitudinem  2  ,  vtl  3.  Uncari^,  BfPK^,. 

guHn  bdrthit  butla^  V^  bute  imminehit  aqu»  aji. 

Mkitudimm  30i  iiaitrm,    Jam  tur  ifiUa,$onder^  . 


i 


^ 


tf^  mrat  i»i»:  itatUditur  ^  fm  ^utk  nitri  fiti 
ri^thitttHMigiiiie  sdtrartftit  fif*  M 'iilUfthm   " 


^^  ^°!  MtrewiM  <pv^Kr  Ji^intat* 


,.    .  r-  -       .. 


I     »«: 


i«  »<^ 


"vsUdhr  ndhafio  ad  Utcra  tubi  j  pr«ci(e  a  cerco 
parriom  plexu  9  &  figura  provcniet^s  j  tiafn 
ceiifuenint^  Aliqui  particuras  fluidprum  an«i^ 
gotformes  alrernis  cavitatibus,  &  promincn'- 
riis  vjtri  veJatinfigi,  partem  bohderis  arnit- 
teVe ,  ac  proptcrea  a  vicfnis  fluidi  cotumnig 
ultra  Kbellam  attolli.  Placere  ndo  pot^ft 
hasc  ^p^ifito ;  fcio  enim  guttam  per  extimds 
cubr  parietes  defiuentem  ^  &  ad  infimum  b- 
fiium/yitH  iSdatam'  eievari  intra  tubum  fine 
adm!b|citifo  vicin^s  ullius  cotumnae^  Scio 
Item :  a^aam  in  e^trado  tubulo  fufpenfam 
filfDitide  aefiuere^  fitubus  invertatur. '  .Scio 
dtoii]i3e':'  bleum  raparum  (  omnium  tenacipi 
^n^xw^)tion  elevari  ultra  19.  lineas  i  cuiti 
intibrea  raiiius  tenaxoleum  vitrioU  ^lti^urgat; , 
pi*6p^'*7;iinea$.\  'Dices:  Fluida  re  vera 
adW^rfefcuht  vWb  j  ergo.  Rtddam  tga  :  ad*. 
hac^ifcurtt,  hon  tatnen  oh  pkxum,  a^^ffiram 
pdfftium  r  fecus  verfo  tubuio  non  deicende^ 

rciit/-  ;-:^^*-  '--  V       .>      '  : 

'■*''-':§,-2f4,;''&d nt^ue  ftttUum a!iMoJ  eUBri' 
um  m  eiiip'^  itfvm  JuUi  s  qaoa  cvbcitae 
ui|o'  JaUA&tff  8e  Miepti  experimcnto ,  qai 
curii  'tliibdjrb    capillari   copiofain   ma^eriaiif ' 

hil* 


48^  Sd^oIT,  OputPI^, 

raiS»  .  ^:  ^  3  fii  ^  "'.'laDi^  sjiioqo  61:. 

iifiif  «k#'  cpcplibnltttr  '«mntt'  p^fioaittvai^ 

^icat  C'2i4>. ,  a!u  txpltaitd  dabo'SUi(^i 
ft^ucntc.     '  '         ^^  '    '-*  ^^  ^^^^^^' 

:'.  Scipl.  bpfoiul.  ${  attraaid  tulri  fit  c»'|i.0^'|U 
i^c^nutj^uidoriim  fu^ra  libellam  ,  clcvan  dcbct  irt«i/ 
diun.n^.  qiP^o  per  intimos  parietcs  tdbi^  .^  cd/irii^ 
Pfir  extimos  t  naxn  vis  trahens  edam  mdteculT^  in^cx^ 
tuna  vjtri.  yipcrhcic  conltitutis  tribaenda  elt  *l  :  -.^oi^ 
ti}teai  ^leyatur,  aut  Verb  noH  rfi«tf  y//^'  elcmur^'c»-* 
tcrnc^  ^uam  Tnterne ;  ci^p.    \\.  l^cbeVcf  WaiorT^-^ 


m»  Ia,£j|ritiia  rqperneie  una  duutaxdt  guct^  luitineri  > 


lut  trih^ji  nPA  po.tcU  tr^Rcnti  yitra,     8ane^|^qui^^jtt^^^ 
1^1  Mqyur^  fc  fniituo  trahunt,  Merc35|uJ  n^^^ 
l^it  in  tubis  eapilIarjDus  (niu  rortyj[ebojllit>sjj.  j^r^Qj,^ 
«  pari,      rV.    Vjs  attra6liva  jn  cpderiV  ,jfiiBfli  c«  c^p- ^ 
iVni,.]Wn]?cr<iuc  cadcm ;  fem^     U^^uc|m^^^  g^fis^ 


Imud  iitti  doeet  uhviA  AbtJchef^cAkna»  ,  VL   Ci^ift 
.vis  attra^iya  reipondeat  maffis  trahentibtis  >  altioreni 
c({e  oportet  afcenrum  in  tnbis  longioribus,  aut  craC 
.    lioribus ,   guam  in  ailis ,  qporum  n^afla  minor  fs&^  (ed 
^  diameter  eadem. '  iniud  vero  adrerfitur  «ic|Jeilenti«  ; 
wgov      VII.  Admiffa  btfclententia  i^ri^iviA^  elevaret. 
ftiaBquaLes.  quancitaces  ejnsdem  fluidi , .  qood  (oiHncnri^ 
noti  po^«    ^u  Ak  Si  tttbps  idem  jaot  rt9%  ^,  jam  «£«» . 
7ijM  a<|nis  imnuttatur,  ^o^e^^uidum  fvehit^r  «i 
^     maiidem  ahhudifiem  perpmdiculdrem  ,  ac  projinde  plui 
inafTae  continetur  tubo  inciinato »  quam  re£to ;    ergo« 
VlII*  Dici  neq^ic  fluidum  trahi  a  toto  tfibuh  ;    (ecua 
Tis  trahens  ageret  in  diftans,  6c  quantitas  fluidi  eleyati 
vefponderet  numero  molecularum  tubos  cdmjponen» 
•    ^um»     Sed  neque  dici  pote();  clevari  fluidpm  ab  annnm 
la  Juprajlmmatnjfluidifuferfiiemcptt/iitmoi^c  enim 
fiuidum  continenter  evehi  deberet  ab  anniili^  proximif 
ti£que  ad  luinmitatem  tubuU  ;,  c^go.      IX."  Vel  totui 
:t     ^yliuder  Qnidus  tul^o  cpntenjtus  trahitur  a  parietibut 
1,      yitri,  vel  {bluqi  t^nuis  illa|amina,  qa«  proxima  tft 
I ,     ftpcrflciei  internat  tubi.    Si  priipum  ;  datur  aftio  in 
\ :      Utltans.     $i  alterum  :  poterit  Uquidum  fclevatum  rlc- 
1 1     inceps  cxtolli  ufquc  ad  {bmmitatem  tubuli  ;   iiquidnm 
«nim   (cmel  clcvatum  non'nItra  gravitat  decy^tum » 
ijnandoquidem  gravitai  liquidi  elcvati  jam*  ab  attradio« 
«ic.vitri  fupcrata  fuit  i  potcri?  igitur  annulus  fuperiot 
prseyalercjfluidumquc  attollerc.   X.  Si  a£tio  immediati  * 
Vitri  non  pertingat   nifi  ad  minima  jntcrvaUa,  nuUa' 
prorjTus  haberi  poteft  elcvatlo  fluidi  in  tubis  cyliQdri« 
iBJs  ;  cum  enim  annulorura  squal^um  asqualcs  (jnt  vl* 
f es  y  fieri  debct ,  ut  quantum.  annulus  idus  fluidum  - 
urget  ad  a/cenfum  ^  tantundcm  urgeat  primus  ad  de« 
iccnGin) .  iguarc  viribus  Cc  mutuo  elidentibUs  nulla  erit 
fluidi  elcyatiQ.     XI.    At  vcrfq  laltcm  tnbo  liqiiidam 
deflucrc  non  jpoflTct  ad  imum  t^bi  qflium,  quod  antci 
(^mmum  crat^  nlmiruin;  idciptannulus ,  qut  potcnt 
w  floidum  deviu^e^  iiidem  pftjcwi  jBii&  dd)Ct  mdnm 


_  tlrjfe  ,t»ko  fitftliifere*  Jltad  Viero  «p«lcttti«'«^^ 
ilttt^i  cigo;  XH.  in  hy^thtfi  tis  tattwaiva  tiD»ido* 
J>f^  ftuiate  aflriw^evdii  SrtAerBnj  iii  tiibirfftftioribtts,, 
;  qttPHi  ii  c^pttbtfsbotr  j  ijnad  non  rtifiiwiit  ;  tt%pm 
'!jPff  M^vu^.  M.  Vaftioriun  tnhutoriutt  majoi?  efli?'  dcbct 
-:Vfl  W«Sfti«^»  tqti*-fempcr  «ftimatarapar}phftri»v&it 
liAMieltrQ  i  .«ttios^o  cv^W  ikbcfet^i«r  tiibis  rafliwi» 
^^y-  fltein  fefliaas  Viratti»aiv«  eft  Mtitudo^  a&crtfuf • 
S<»iS^*  ^^^^rti^^  akoir  «ffupgit'  in  t<ibis  yaftioti- 
.  itt$,  major  vis  arttiiClsra  flinnoloBuin'  nwjoniiw^^teftH 
tow^  Wni  effefht,  ?  ^ 


,.  « >  f «, 


^lMmiic^  refpondebo*,  jiain  plcraqtieiftai  mnl»4 

j^afi^dcdi,  ac  foUuioncs  inrinoavi  4*  *4^-     ^*  ** 

1 G.  M'  -D-  tfl.  wir  at^icm  elcvatur  «tjuc^alte,  -M  intfa 

<^tumG.«w,  peaitiw  noit  clcvaiiitN/m.  &  C.:  y^Vro 

4i«3r4  llajdam  Mti^  etidtatur  mtcmc  ,  qyfiamMCXtttfne, 

ih.cauj^  cfl;  pari^Ciim  'intetnoruin  vicinita*  ;  'iuti«« 

cnim  (irperficica  mttttio  fc  refpiciunt ,  fcquc' adjuvant. 

Ad  II.  C.  M»  M.  m.  td  Pr.  C*  1 .  p.  A.  ^* ».  intw  tb^ 

bulos  una  duntaxat  gutta  clevatur,  paotto  tAvmxi  m^- 

jor,  quam  qu«  A  iafici^ cxtcrno  vitrt' OiacnmU^ 

€.  h.  pi  qu*  wajor  lion  fit  N*  b.  p.  &  ^r    'Nitel.tec 

commtnifcor;  teflamur  tn?m  Marf^mSy  V^BulgSfge- 

rus  intj^  tubulnm  capil*aremd«varig«ttam  «^a^«*^ttw 

btro  Ju/iineiidam ,  qu»  mtjor.cft  f  prr  ^r^  ra» 

jf,  249. )  .       Ad  Hh  D.  A.  prafvakt;tamcn  «ttraftlia 

Vitri  Q,  A.  non  prarvalct  N.  A.  \&  C. v ,  Cwicrtriiwn  <<b. 

.tinct%  i«  Mercurio  docui  ^r.  IK    Scd  ^jflotmnfas 

Sin  tubii  fcbo  ilUtia  afctndit  Mcccuriiis,  quod  triboca. 

dum  febo ,  cujus  validior  cft  aaic*  in  Nfcrcuriute,  quam 

fit  m^tua  particularuhi  Mcrcurii  aitraaio.      AdlV» 

D.  A    vis  attraaiva  in-codcm  tubo  i^Aconftana  f^late 

Md  idem  jiuidum  C.  A.  sd  dherfa  N.  A.  D;  C.  femper 

fluidaad  candem  aWtiidincm.afttom  dcbcnt,  fi  vis  ftmda 

clcvana  Gttota  at(rM3hvi&i  C.  C,  fi  ta  taiitnm  ^JP^f^ 

jrii>,qua  vitrurt  mwam  ftiidi  attraakmtm  fiipcrat  N;C 


C 


#5»  eflo  (q»ortcf «  afedrfum  te  tub«Iong>otAw,  fi^iN 

(«dmitiiina  5tam  interwiUaN.  M^  Vide  i^frt.  IK» 
ftd VH.  D.A.  vi«  eadcmckmet  iniqoatts  quantita- 
«a  flMdialiter  tmnen  appHcatwC.  As,  eodeiiwnodo»^ 
pUcatas  Kf.  A.  Imnio  ad  rigoreih  l«itt«ndo  fton  eft 
«idem  vis  elevani  in  tnbo  fWiMW,  &  «5o }  nam  ii« 
teao  vi  «tttaai*«  refiftit  Poh  J^»»»''*.*^'*,'!* 
ebUquo  «J*«8iw«.       Ad  Vllfc  C.  I.  p.  A.  Ni^a.  Cbt 

vfluidum  evebi  non  debeat  ad  fimimiiatetn  tnbdri,  legw 
keirt'  y^   " Ad  IX.  «jo  t  AvXKxm  tenueia  ritam' fcmi. 

,  i»am^perft?iei  intini*  «dhetentem  iittmfMk  a9nlm 

itfirtattoltt  (  «r  ^rt.  IX.;  ,  nec  tajnWi  «quorem 

«m /fiwnmuw  luboli  oftiom  «lenri  poflfc^  0*u(feleai 

©^ttquidom  femel  elevatuTO  non  «Inra  gr«vf»t  deor. 

^iMnleeuildKai  tcnaiffimam  l«»ai««l  vitto  i^ceriteln 

C  paoffaL  (eoundum  cyUndtwn  mediailt ,  q««  non»' 

•oitraaiva,  &d  Hiat»«  coh«renti«  «iftt»r«jdt  JN.^ulHL 

^e^   ^AidXi  fohitiittieffl  dedi  vfjfifi*.  W£.   _pici  in. 

terea  poteft  t -tnrsr' fltMto)<»ilp  primi ,  *a»i  «  ««- 

-AiJit,^e<>queipf«  pssmtee  vis  «nnnli  ?tii ,  qui  emt* 

awK.&twredebefCA.  non  pf«valet  N.  A.  &  C. 

AdiXL  WuA^^ad  ft:.-D.  A.  idom  «nnolos  potensefie 

-  ddiet  A«Muin  vcrfo  tubo  jgiftinere ,  finon  iiceedat  vJ» 

nofaliquoref»:  uffgewid  <le(cenfam  C.  A.  fi:  aceedat 

N.  A.&C;  j«tt/i»«i^  ««icedit»i»«nnuli  infifi  ewn,  «jui 

.^rtdj/liqnof em  &ftiiiebat,  continentwr  fiti , -qtoe  eli& 

jwnfaitryicuiniemid.anHuittt proximc  iuperior  trahat 

Jlijidum.  ann&lotx^lcnm  IncUium ,  «nnultt»  «tttem  ei. 

..creiUas  vibifl^  tvahat  ftuidom  priore  illo  eontentmrt, 

vt(««;eoiom.  fis  impediiiat',  ficqoe  «nnala  infi»  firfti- 

jOentem;  pofin»  efteanm  «oift^tttr.    Reciirrant  ^ 


484 


•^W      w^^^^W^^  •  j9^^^99^^  ^&^wW% 


id  VUa  «qioU  proximi  eaga  pondere  fliiidi  eoDQ>ictfihi 
icm.  •  ^Ad  XIL  N.  Seqai  M.  ad  Pr.  D.  A«  vaftiortifn 
«nnaloruia  inayor  cflc  dcbct  via  alfoiutd  C.  A.  rej^c^i^K 
pM  N.  A.  eaitflaleai  cadem  ratioae  D.^  vis  trabcns  aijo^ 
bu4  cft  Qt  peri[>herta  C  A.  re^e^iva  N.  A.  &  C^ 
Iftius  caoflalcm  ror(iitii.D«  effe^his  visattradivx  cft  idm 
^mdo  aftcoflM  duSa  in  bafim  C*  A.  altimd^  fimpUmer 
^,  A.  ft  C«  citriora  hsc  ficnt  ex  ^  849.  CarM.  11% 
j4J  Covfirt»^  N.  Sequ.  A.  elFe^os  oiajoris  ^it^aifilum 
l<  cft  major  fluidi  portioy  qus  dcvator. 

Cauffa  ajceufum  flaidoroin  ej^ciens  iaiijpme  fer$U 
fHt ;  rx  ea  qtnppc  dependet^  quod  minores  fluidotum  for^ 
fiaues  fi  a/d  liiellam  nosi  compouant  %  quod  aqua  ccrpj»rm 
^i0cdam  bumeStet ,  ab  aliu  veluti  refugiat :  quod  Uquo^ 
tes  iu  augftflif.  vafis  curva  fuporficie  termsnefuur  i  quod 
^ngim^  eUydmia  y  faccbarum  ^  cineres  Efc-  Mtrfeuda 
mbuatu;  fuod  uauvus  fnccue  per  plantarum  fibras  cemm, 
nsect :  quod  bumores  iu  glanduUs  vivesititim  corporutt^ 
varie  feceruantur  :  quodfahgttU  per  vafa  atmftijl 
fima  jugiser  dijiribuatur^  &*  bi9  ifjj^aia  ma^ 


lr*l 


j 


O.  A.  M.  D.  G. 


ff^t,*\h'if*,    ^o^t-f 


\ 


« 


V 

r 


-1 


i 


H 

«t 

I* 

if 

U 


i 


I 

1 


% 


V, 


s. 


^ 


*";^f 


•1 


< 


/■ 
\ 


N, 


/- 


■     •    1.1-11  fK     ••<■••  ^'m  I 


I        ■  ^ 


■^ 


./ 


•         .^ 


Z' 


\ 


/ 


f       "1 


V.        - 


X 


\ 


; 


'\ 


/■     )     ( 


t 


J 


^  /         ^ 


,y 


y^^ 


/ 


•  * 


■»> 


V-' 


<  ( 


-.    ) 


>  < 


> . 


W 


-    r 


.  V 


t: 


\       ^ 


f' 


•> 


i» 


V 


' 


''V 


\ 


.  .■/ 


/  ^ 


\         V 


)-  \ 


r 


',<      V 


J'- 


/ 


■NO. 


"■-  -»  ... 


/-     — ^  i' ,  '< 


»3 ^ 


■  ii     ■■  il 


.**/ 


f  •  -r- 


•  \ 


yMLXI^^iTY  OF  MICHIQAN 


■■*  ^  <  ,.^     \  • 


3  9015064484846 


1  ^  T<i-  V  nr-  j^ 


"^"  ^'      »   .  'TT  * 


1  ' 


M 


^♦Xi', 


■^ 


,-:^-v^ 


%\ 


<^ 


vJ 


V    --^ 


«     ^.  » 


■^»." 


N..  •; 


k 


s. 


I  • 


'^ 


»►.. 


\ 


N 


L 


\ 


V 


# 


Ai. 


Wto 


ift. 


dHi 


^'•^rfr